Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems. PMID:26632587
Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M.; Eric Tai, M.; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Optimal Correlations in Many-Body Quantum Systems
NASA Astrophysics Data System (ADS)
Amico, L.; Rossini, D.; Hamma, A.; Korepin, V. E.
2012-06-01
Information and correlations in a quantum system are closely related through the process of measurement. We explore such relation in a many-body quantum setting, effectively bridging between quantum metrology and condensed matter physics. To this aim we adopt the information-theory view of correlations and study the amount of correlations after certain classes of positive-operator-valued measurements are locally performed. As many-body systems, we consider a one-dimensional array of interacting two-level systems (a spin chain) at zero temperature, where quantum effects are most pronounced. We demonstrate how the optimal strategy to extract the correlations depends on the quantum phase through a subtle interplay between local interactions and coherence.
Experimental quantum simulation of entanglement in many-body systems.
Zhang, Jingfu; Wei, Tzu-Chieh; Laflamme, Raymond
2011-07-01
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudoentanglement. The observed pseudoentanglement for a small-size system already displays a singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators. PMID:21797528
Geodesic paths for quantum many-body systems
NASA Astrophysics Data System (ADS)
Tomka, Michael; Souza, Tiago; Rosenberg, Steve; Kolodrubetz, Michael; Polkovnikov, Anatoli
The quantum length is a distance between parameter-dependent eigenstates of an adiabatically driven quantum system. Its associated metric has many intriguing properties, for example it is related to the fidelity susceptibility, an important quantity in the study of quantum phase transitions. The metric also appears as the leading adiabatic correction of the energy fluctuations of a quantum system and gives rise to a time-energy uncertainty principle and a geometric interpretation of time. The adiabatic response of an open quantum system can as well be expressed through this metric. Further, the quantum length introduces the notion of Riemannian geometry to the manifold of eigenstates and hence allows one to define geodesics in parameter space. We study the geodesics in parameter space of certain quantum many-body systems, emerging from this quantum distance. These geodesic paths provide a well-defined optimal control protocol on how to drive the system's parameters in time, to get from one eigenstate to another. Generating optimal evolution plays a central role in quantum information technology, adiabatic quantum computing and quantum metrology. Swiss National Science Foundation (SNSF).
Boundary driven open quantum many-body systems
Prosen, Tomaž
2014-01-08
In this lecture course I outline a simple paradigm of non-eqjuilibrium quantum statistical physics, namely we shall study quantum lattice systems with local, Hamiltonian (conservative) interactions which are coupled to the environment via incoherent processes only at the system's boundaries. This is arguably the simplest nontrivial context where one can study far from equilibrium steady states and their transport properties. We shall formulate the problem in terms of a many-body Markovian master equation (the so-called Lindblad equation, and some of its extensions, e.g. the Redfield eqaution). The lecture course consists of two main parts: Firstly, and most extensively we shall present canonical Liouville-space many-body formalism, the so-called 'third quantization' and show how it can be implemented to solve bi-linear open many-particle problems, the key peradigmatic examples being the XY spin 1/2 chains or quasi-free bosonic (or harmonic) chains. Secondly, we shall outline several recent approaches on how to approach exactly solvable open quantum interacting many-body problems, such as anisotropic Heisenberg ((XXZ) spin chain or fermionic Hubbard chain.
Periodically driven ergodic and many-body localized quantum systems
Ponte, Pedro; Chandran, Anushya; Papić, Z.; Abanin, Dmitry A.
2015-02-15
We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.
Time evolution of open quantum many-body systems
NASA Astrophysics Data System (ADS)
Overbeck, Vincent R.; Weimer, Hendrik
2016-01-01
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding very good quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics towards the steady state. We further quantify this non-Markovianity and find it to be closely connected to an information-theoretical measure of quantum and classical correlations.
Dynamics in many-body localized quantum systems without disorder
NASA Astrophysics Data System (ADS)
Schiulaz, Mauro; Silva, Alessandro; Müller, Markus
2015-05-01
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration is nonperturbatively slow in the hopping strength, and potentially genuinely nonergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, which are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with the system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonant configurations. We suggest experimental realizations and methods to observe the discussed nonergodic dynamics.
Classical simulation of quantum many-body systems
NASA Astrophysics Data System (ADS)
Huang, Yichen
Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance. It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood. Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods. Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).
Quantum phase transition in strongly correlated many-body system
NASA Astrophysics Data System (ADS)
You, Wenlong
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions (QPTs), driven by experimental advance on the cuprate superconductors, the heavy fermion materials, organic conductors, Quantum Hall effect, Fe-As based superconductors and other related compounds. It is clear that strong electronic interactions play a crucial role in the systems of current interest, and simple paradigms for the behavior of such systems near quantum critical points remain unclear. Furthermore, the rapid progress in Feshbach resonance and optical lattice provides a flexible platform to study QPT. Quantum Phase Transition (QPT) describes the non-analytic behaviors of the ground-state properties in a many-body system by varying a physical parameter at absolute zero temperature - such as magnetic field or pressure, driven by quantum fluctuations. Such quantum phase transitions can be first-order phase transition or continuous. The phase transition is usually accompanied by a qualitative change in the nature of the correlations in the ground state, and describing this change shall clearly be one of our major interests. We address this issue from three prospects in a few strong correlated many-body systems in this thesis, i.e., identifying the ordered phases, studying the properties of different phases, characterizing the QPT points. In chapter 1, we give an introduction to QPT, and take one-dimensional XXZ model as an example to illustrate the QPT therein. Through this simple example, we would show that when the tunable parameter is varied, the system evolves into different phases, across two quantum QPT points. The distinct phases exhibit very different behaviors. Also a schematic phase diagram is appended. In chapter 2, we are engaged in research on ordered phases. Originating in the work of Landau and Ginzburg on second-order phase transition, the spontaneous symmetry breaking induces nonzero expectation of field operator, e.g., magnetization M in the Ising model, and then we say long range order (LRO) exists in the system. LRO plays a key role in determining the ordered-disorder transition. Thereby, we investigate two-dimensional 120 orbital-only model to present how to extract the information of LRO in a pedagogical manner, by applying the reflection positivity method introduced by Dyson, Lieb, and Simon. We rigorously establish the existence of an anti-ferromagnetic like transverse orbital long-range order in the so called two-dimensional 120 model at zero temperature. Next we consider possible pairings in the family of FeAs-based ReO1--xFxFeAs (Re=La, Nd, Ce, Pr, etc.) high-temperature superconductors. We build some identities based on a two-orbital model, and obtained some constraints on a few possible pairings. We also establish the sufficient conditions for the coexistence of two superconducting orders, and we propose the most favorable pairings around half filling according to physical consideration. In chapter 3, we present a quantum solvation process with solvent of fermion character based on the one-dimensional asymmetric t-J-Jz model. The model is experimental realizable in optical lattices and exhibits rich physics. In this work, we show that there exist two types of phase separations, one is driven by potential energy while the other by kinetic energy. In between, solvation process occurs. Analytically, we are able to obtain some rigorous results to understand the underlying physics. Numerically, we perform exact diagonalization and density matrix renormalization group calculations, accompanied by detailed finite size analysis. In chapter 4, we explore several characterizations of QPT points. As distinguished from the methods in condensed-matter physics, we give much attention to understand QPT from the quantum information (QI) point of view. The perspective makes a new bridge between these two fields. It no only can facilitate the understanding of condensed-matter physics, but also provide the prominent playground for the quantum information theory. They are fidelity susceptibility and reduced fidelity susceptibility. We establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through fidelity susceptibility and show that the evaluation of fidelity in terms of susceptibility is facilitated by using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium. Furthermore, we show that the reduced fidelity susceptibility in the family of one-dimensional XY model obeys scaling law in the vicinity of quantum critical points both analytically and numerically. The logarithmic divergence behavior suggests that the reduced fidelity susceptibility can act as an indicator of quantum phase transition.
Dissipation and dynamics in quantum many-body systems
NASA Astrophysics Data System (ADS)
Barker, Brent Wendolyn
In this thesis, we simulate the time evolution of quantum many-body systems and use comparisons to experimental data in order to learn more about the properties of nuclear matter and understand better the dynamical processes in central nuclear collisions. We further advance the development of a nonequilibrium Green's function description of both central nuclear collisions and Bose-Einstein Condensates. First in the thesis, we determine the viscosity of nuclear matter by adjusting the in-medium nucleon-nucleon cross section (IMNNCS) in our BUU transport model until the simulation results match experimental data on nuclear stopping in central nuclear collisions at intermediate energies. Then we use that cross section to calculate the viscosity self-consistently. We also calculate the ratio of shear viscosity to entropy density to determine how close the system is to the proposed universal quantum lower limit. Next, we use the same BUU transport model to isolate the protons emitted early in a central nuclear collision at intermediate energy, as predicted in the model, using a filter on high transverse momentum, and we show the effect on the source function. We predict a recontraction of protons at late times in the central collision of 112Sn+112Sn at 50 MeV/nucleon that results in a resurgence of emission of protons and show how to use the transverse momentum filter and the source function to test this prediction in experiment. Next, we develop an early implementation of a more fully quantal transport model than the BUU equations, with our sights set on solving central nuclear collisions in 3D using nonequilibrium Green's functions. In our 1D, mean field, density matrix model, we demonstrate the initial state preparation and collision of 1D nuclear "slabs". With the aim of reducing the computational cost of the calculation, we show that we can neglect far off-diagonal elements in the density matrix without affecting the one-body observables. Further, we describe a method of recasting the density matrix in a rotated coordinate system, enabling us to not only ignore the irrelevant matrix elements in the time evolution, but also avoid computing them completely, reducing the computational cost. As an added benefit, we find that the rotation allows us to partially decouple the position and momentum discretization, permitting access to arbitrary regimes of kinetic energy without altering the resolution and range of the 1D box in position space. Finally, we exhibited the wide applicability of this density matrix approach by applying it to a system of 2000 ultracold 87Rb atoms in a Bose-Einstein condensate, as described by the Gross-Pitaevskii equation, successfully achieving a stable state in a harmonic oscillator trap.
Characterizing and quantifying frustration in quantum many-body systems.
Giampaolo, S M; Gualdi, G; Monras, A; Illuminati, F
2011-12-23
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration. PMID:22243147
General coordinate invariance in quantum many-body systems
NASA Astrophysics Data System (ADS)
Brauner, Tom; Endlich, Solomon; Monin, Alexander; Penco, Riccardo
2014-11-01
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the background metric and gauge fields, first introduced by Son and Wingate in 2005 and refined in subsequent works, follow naturally from our framework. Our approach makes it clear that Galilei or Poincar symmetry is by no means a necessary prerequisite for making the theory invariant under coordinate diffeomorphisms. General covariance merely expresses the freedom to choose spacetime coordinates at will, whereas the true, physical symmetries of the system can be separately implemented as "internal" symmetries within the vielbein formalism. A systematic way to implement such symmetries is provided by the coset construction. We illustrate this point by applying our formalism to nonrelativistic s -wave superfluids.
Localization and Glassy Dynamics Of Many-Body Quantum Systems
Carleo, Giuseppe; Becca, Federico; Schiró, Marco; Fabrizio, Michele
2012-01-01
When classical systems fail to explore their entire configurational space, intriguing macroscopic phenomena like aging and glass formation may emerge. Also closed quanto-mechanical systems may stop wandering freely around the whole Hilbert space, even if they are initially prepared into a macroscopically large combination of eigenstates. Here, we report numerical evidences that the dynamics of strongly interacting lattice bosons driven sufficiently far from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states. The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon. We argue that the resulting long-lived inhomogeneities are responsible for the lack of thermalization observed in large systems. Such a rich phenomenology could be experimentally uncovered upon probing the out-of-equilibrium dynamics of conveniently prepared quantum states of trapped cold atoms which we hereby suggest. PMID:22355756
Localization and glassy dynamics of many-body quantum systems.
Carleo, Giuseppe; Becca, Federico; Schiró, Marco; Fabrizio, Michele
2012-01-01
When classical systems fail to explore their entire configurational space, intriguing macroscopic phenomena like aging and glass formation may emerge. Also closed quanto-mechanical systems may stop wandering freely around the whole Hilbert space, even if they are initially prepared into a macroscopically large combination of eigenstates. Here, we report numerical evidences that the dynamics of strongly interacting lattice bosons driven sufficiently far from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states. The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon. We argue that the resulting long-lived inhomogeneities are responsible for the lack of thermalization observed in large systems. Such a rich phenomenology could be experimentally uncovered upon probing the out-of-equilibrium dynamics of conveniently prepared quantum states of trapped cold atoms which we hereby suggest. PMID:22355756
Dissipative effects in dipolar, quantum many-body systems
NASA Astrophysics Data System (ADS)
Safavi-Naini, Arghavan; Capogrosso-Sansone, Barbara; Rey, Ana Maria
2015-03-01
We use Quantum Monte Carlo simulations, by the Worm algorithm, to study the ground state phase diagram of two-dimensional, dipolar lattice bosons where each site is coupled, via density operators, to an external reservoir. A recent related study of the XXZ model with ohmic coupling to an external reservoir reported the existence of a bath-induced Bose metal phase in the ground state phase diagram away from half filling, and a Luttinger liquid and a charge density wave at half-filling. Our work extends this methodology to higher dimensional systems with long-range interactions. In the case of hard-core bosons, our method can be applied to experimental systems featuring dipolar fermionic molecules in the presence of losses. This work utilized the Janus supercomputer, which is supported by the NSF (award number CNS-0821794) and the University of Colorado Boulder, and is a joint effort with the University of Colorado Denver and the National Center for Atmospheric Research, as well as OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma. NIST, JILA-NSF-PFC-1125844, NSF-PIF-1211914, NSF-PHY11-25915, ARO, ARO-DARPA-OLE, AFOSR, AFOSR-MURI.
Preparing ground states of quantum many-body systems on a quantum computer
NASA Astrophysics Data System (ADS)
Poulin, David
2009-03-01
The simulation of quantum many-body systems is a notoriously hard problem in condensed matter physics, but it could easily be handled by a quantum computer [4,1]. There is however one catch: while a quantum computer can naturally implement the dynamics of a quantum system --- i.e. solve Schr"odinger's equation --- there was until now no general method to initialize the computer in a low-energy state of the simulated system. We present a quantum algorithm [5] that can prepare the ground state and thermal states of a quantum many-body system in a time proportional to the square-root of its Hilbert space dimension. This is the same scaling as required by the best known algorithm to prepare the ground state of a classical many-body system on a quantum computer [3,2]. This provides strong evidence that for a quantum computer, preparing the ground state of a quantum system is in the worst case no more difficult than preparing the ground state of a classical system. 1 D. Aharonov and A. Ta-Shma, Adiabatic quantum state generation and statistical zero knowledge, Proc. 35th Annual ACM Symp. on Theo. Comp., (2003), p. 20. F. Barahona, On the computational complexity of ising spin glass models, J. Phys. A. Math. Gen., 15 (1982), p. 3241. C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani, Strengths and weaknessess of quantum computing, SIAM J. Comput., 26 (1997), pp. 1510--1523, quant-ph/9701001. S. Lloyd, Universal quantum simulators, Science, 273 (1996), pp. 1073--1078. D. Poulin and P. Wocjan, Preparing ground states of quantum many-body systems on a quantum computer, 2008, arXiv:0809.2705.
Thermal states of random quantum many-body systems
NASA Astrophysics Data System (ADS)
Nakata, Yoshifumi; Osborne, Tobias J.
2014-11-01
We study a distribution of thermal states given by random Hamiltonians with a local structure. We show that the ensemble of thermal states monotonically approaches the unitarily invariant ensemble with decreasing temperature if all particles interact according to a single random interaction and achieves a state t -design at temperature O ( 1 /log (t )) . For the system where the random interactions are local, we show that the ensemble achieves a state 1-design. We then provide numerical evidence indicating that the ensemble undergoes a phase transition at finite temperature.
Numerical Simulations of Quantum Many-body Systems
Scalapino, Douglas J. Sugar, Robert L.
1998-04-20
The goals of our DOE work were to develop numerical tools in order to (1) determine the actual phase of particular many-electron models and (2) to understand the underlying mechanisms responsible for the observed phases. Over the years, DOE funds provided support for a number of graduate students and postdoctoral fellows who have gone on to continue and extend this effort. Looking back, they were more successful in determining the types of correlations that developed in particular models and less successful in establishing the underlying mechanisms. For example, they found clear evidence for antiferromagnetism, d{sub x{sup 3}-y{sup 2}}-pairing correlations, and stripes in various t-t{prime}-J and Hubbard models. Here, the stripes consisted of 1/2-filled domain walls of holes separated by {pi}-phase shifted antiferromagnetic regions. They found that a next-near-neighbor hopping t{prime} with t{prime}/t > 0 suppressed the stripes and favored the d{sub x{sup 3}-y{sup 2}}-pairing correlations. They studied a model of a CuO, 2-leg ladder and found that d{sub x{sup 3}-y{sup 2}} correlations formed when the system was doped with either electrons or holes. Another example that they studied was a two-dimensional spin 1/2 easy plane model with a near-neighbor exchange J and a four-site ring exchange K. In this J-K model, as K/J is increased, one moves from XY order to stripe order and to Ising antiferromagnetic order. They are still exploring the unusual transition between the Xy and striped phase. The key feature that we found was that strongly-correlated, many-electron systems are 'delicately balanced' between different possible phases. They also believe that their work provides strong support in favor of Anderson's suggestion that the Hubbard model contains the basic physics of the cuprates. That is, it exhibits antiferromagnetism, d{sub x{sup 3}-y{sup 2}}-pairing correlations, and stripes as the half-filled model is doped with holes. They were not as successful in determining the basic mechanisms. Specifically, they sought to determine the basic pairing mechanism. They tried various approaches and concluded that the spin-fluctuations play a central role. However, it was only recently, with Professor Mark Jarrell (UC) and Dr. Thomas Maier (ORNL), that they have found clear evidence that the pairing is mediated by an S = 1 particle-hole fluctuation.
A quantum many-body spin system in an optical lattice clock.
Martin, M J; Bishof, M; Swallows, M D; Zhang, X; Benko, C; von-Stecher, J; Gorshkov, A V; Rey, A M; Ye, Jun
2013-08-01
Strongly interacting quantum many-body systems arise in many areas of physics, but their complexity generally precludes exact solutions to their dynamics. We explored a strongly interacting two-level system formed by the clock states in (87)Sr as a laboratory for the study of quantum many-body effects. Our collective spin measurements reveal signatures of the development of many-body correlations during the dynamical evolution. We derived a many-body Hamiltonian that describes the experimental observation of atomic spin coherence decay, density-dependent frequency shifts, severely distorted lineshapes, and correlated spin noise. These investigations open the door to further explorations of quantum many-body effects and entanglement through use of highly coherent and precisely controlled optical lattice clocks. PMID:23929976
Classical simulation of quantum many-body systems with a tree tensor network
Shi, Y.-Y.; Duan, L.-M.; Vidal, G.
2006-08-15
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.
NON-EQUILIBRIUM DYNAMICS OF MANY-BODY QUANTUM SYSTEMS: FUNDAMENTALS AND NEW FRONTIER
DeMille, David; LeHur, Karyn
2013-11-27
Rapid progress in nanotechnology and naofabrication techniques has ushered in a new era of quantum transport experiments. This has in turn heightened the interest in theoretical understanding of nonequilibrium dynamics of strongly correlated quantum systems. This project has advanced the frontiers of understanding in this area along several fronts. For example, we showed that under certain conditions, quantum impurities out of equilibrium can be reformulated in terms of an effective equilibrium theory; this makes it possible to use the gamut of tools available for quantum systems in equilibrium. On a different front, we demonstrated that the elastic power of a transmitted microwave photon in circuit QED systems can exhibit a many-body Kondo resonance. We also showed that under many circumstances, bipartite fluctuations of particle number provide an effective tool for studying many-body physics—particularly the entanglement properties of a many-body system. This implies that it should be possible to measure many-body entanglement in relatively simple and tractable quantum systems. In addition, we studied charge relaxation in quantum RC circuits with a large number of conducting channels, and elucidated its relation to Kondo models in various regimes. We also extended our earlier work on the dynamics of driven and dissipative quantum spin-boson impurity systems, deriving a new formalism that makes it possible to compute the full spin density matrix and spin-spin correlation functions beyond the weak coupling limit. Finally, we provided a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in the case of a spinless dissipative resonant-level model. This project supported the research of two Ph.D. students and two postdoctoral researchers, whose training will allow them to further advance the field in coming years.
Quantum chaos in many-body systems: what can we learn from the Ce atom?
NASA Astrophysics Data System (ADS)
Flambaum, V. V.; Gribakina, A. A.; Gribakin, G. F.; Ponomarev, I. V.
1999-07-01
Results of an extensive study of a real quantum chaotic many-body system - the Ce atom - are presented. We discuss the origins of the quantum chaotic behaviour of the system, analyse statistical and dynamical properties of the multi-particle chaotic eigenstates and consider matrix elements or transition amplitudes between them. We show that based on the universal properties of the chaotic eigenstates a statistical theory of finite few-particle systems with strong interaction can be developed. We also discuss such important physical effects as enhancement of weak perturbations in many-body quantum chaotic systems, distribution of single-particle occupation numbers and its deviations from the standard Fermi-Dirac shape, and ways of introducing statistical temperature-based description in such systems.
Schuch, Norbert; Wolf, Michael M.; Cirac, J. Ignacio; Verstraete, Frank
2008-02-01
We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.0.
Nonlocality in many-body quantum systems detected with two-body correlators
NASA Astrophysics Data System (ADS)
Tura, J.; Augusiak, R.; Sainz, A. B.; Lücke, B.; Klempt, C.; Lewenstein, M.; Acín, A.
2015-11-01
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states-ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
Isolated many-body quantum systems far from equilibrium: Relaxation process and thermalization
Torres-Herrera, E. J.; Santos, Lea F.
2014-10-15
We present an overview of our recent numerical and analytical results on the dynamics of isolated interacting quantum systems that are taken far from equilibrium by an abrupt perturbation. The studies are carried out on one-dimensional systems of spins-1/2, which are paradigmatic models of many-body quantum systems. Our results show the role of the interplay between the initial state and the post-perturbation Hamiltonian in the relaxation process, the size of the fluctuations after equilibration, and the viability of thermalization.
Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems
Stimming, H.-P.; Mauser, N. J.; Mazets, I. E.
2010-07-02
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.
Equivalent dynamical complexity in a many-body quantum and collective human system
NASA Astrophysics Data System (ADS)
Johnson, Neil F.; Ashkenazi, Josef; Zhao, Zhenyuan; Quiroga, Luis
2011-03-01
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding of Fratini et al. concerning quantum many-body effects in cuprate superconductors (i.e. scale of 10-9 - 10-4 meters and 10-12 - 10-6 seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism (i.e. scale of 103 - 106 meters and 104 - 108 seconds), (iii) shows consistency with various established empirical facts for financial markets, neurons and human gangs and (iv) makes microscopic sense for each application. Our findings also suggest that a potentially productive shift can be made in Complexity research toward the identification of equivalent many-body dynamics in both classical and quantum regimes.
Thermopower as a tool to investigate many-body effects in quantum systems
Kristinsdóttir, L. H.; Bengtsson, J.; Reimann, S. M.; Wacker, A.; Linke, H.
2014-08-25
Measuring the thermopower of a confined quantum system reveals important information about its excitation spectrum. Our simulations show how this kind of transport spectroscopy is able to extract a clear signal for the onset of Wigner localization in a nanowire segment. This demonstrates that thermopower measurements provide a tool for investigating complex many-body quantum effects, which is less intrusive than the usual charge-stability diagram as no high source-drain bias is required. While the effect is most pronounced for weak tunnel coupling and low temperatures, the excited states also significantly affect the thermopower spectrum at moderate temperature, adding distinct features to the characteristic thermopower lineshape.
Single-shot simulations of dynamic quantum many-body systems
NASA Astrophysics Data System (ADS)
Sakmann, Kaspar; Kasevich, Mark
2016-05-01
Single experimental shots of ultracold quantum gases sample the many-particle probability distribution. In a few cases such single shots could be successfully simulated from a given many-body wavefunction, but for realistic time-dependent many-body dynamics this has been difficult to achieve. Here, we show how single shots can be simulated from numerical solutions of the time-dependent many-body Schrödinger equation. Using this approach, we provide first-principle explanations for fluctuations in the collision of attractive Bose-Einstein condensates (BECs), for the appearance of randomly fluctuating vortices and for the centre-of-mass fluctuations of attractive BECs in a harmonic trap. We also show how such simulations provide full counting distributions and correlation functions of any order. Such calculations have not been previously possible and our method is broadly applicable to many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.
Editorial: Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Cazalilla, M. A.; Rigol, M.
2010-05-01
The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and understand many-body quantum systems. This focus issue of New Journal Physics brings together both experimentalists and theoreticians working on these problems to provide a comprehensive picture of the state of the field. Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems Contents Spin squeezing of high-spin, spatially extended quantum fields Jay D Sau, Sabrina R Leslie, Marvin L Cohen and Dan M Stamper-Kurn Thermodynamic entropy of a many-body energy eigenstate J M Deutsch Ground states and dynamics of population-imbalanced Fermi condensates in one dimension Masaki Tezuka and Masahito Ueda Relaxation dynamics in the gapped XXZ spin-1/2 chain Jorn Mossel and Jean-Sébastien Caux Canonical thermalization Peter Reimann Minimally entangled typical thermal state algorithms E M Stoudenmire and Steven R White Manipulation of the dynamics of many-body systems via quantum control methods Julie Dinerman and Lea F Santos Multimode analysis of non-classical correlations in double-well Bose-Einstein condensates Andrew J Ferris and Matthew J Davis Thermalization in a quasi-one-dimensional ultracold bosonic gas I E Mazets and J Schmiedmayer Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics Cavan Stone, Yassine Ait El Aoud, Vladimir A Yurovsky and Maxim Olshanii On the speed of fluctuations around thermodynamic equilibrium Noah Linden, Sandu Popescu, Anthony J Short and Andreas Winter A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states M Cramer and J Eisert Quantum quench dynamics of the sine-Gordon model in some solvable limits A Iucci and M A Cazalilla Nonequilibrium quantum dynamics of atomic dark solitons A D Martin and J Ruostekoski Quantum quenches in the anisotropic spin-1⁄2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler and Ehud Altman Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics Michael Moeckel and Stefan Kehrein Quantum quenches in integrable field theories Davide Fioretto and Giuseppe Mussardo Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point A Bermudez, L Amico and M A Martin-Delgado Thermometry with spin-dependent lattices D McKay and B DeMarco Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy Martin Eckstein and Marcus Kollar Sudden change of the thermal contact between two quantum systems J Restrepo and S Camalet Reflection of a Lieb-Liniger wave packet from the hard-wall potential D Jukić and H Buljan Probing interaction-induced ferromagnetism in optical superlattices J von Stecher, E Demler, M D Lukin and A M Rey Sudden interaction quench in the quantum sine-Gordon model Javier Sabio and Stefan Kehrein Dynamics of an inhomogeneous quantum phase transition Jacek Dziarmaga and Marek M Rams
Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit.
Prosen, T
1999-10-01
We study a generic but simple nonintegrable quantum many-body system of locally interacting particles, namely, a kicked-parameter (t,V) model of spinless fermions on a one-dimensional lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). The statistical properties of the dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in the thermodynamic limit are considered as the kick parameters (which control the degree of nonintegrability) are varied. We find and demonstrate ballistic transport and nonergodic, nonmixing dynamics (implying infinite conductivity at all temperatures) in the integrable regime of zero or very small kick parameters, and more generally and importantly, also in the nonintegrable regime of intermediate values of kicked parameters, whereas only for sufficiently large kick parameters do we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness D) which controls the phase transition from nonmixing and nonergodic dynamics (ordered phase, D>0) to mixing and ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find exponential decay of time correlation functions in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time-averaged observables. PMID:11970231
Rahman Prize Talk: Pushing the frontier in the simulation of correlated quantum many body systems
NASA Astrophysics Data System (ADS)
Troyer, Matthias
Amazing progress in the simulation of correlated quantum many body systems has been achieved in the past two decades by combining significant advances in new algorithms with efficient implementations on ever faster supercomputers. This has enabled the accurate simulation of an increasing number of problems and helped settle many open questions. I will review a selection of results that my collaborators and I have worked on, from quantum phase transitions in quantum magnets, over supersolidity of bosons in lattice models and Helium-4 to recent simulations of correlated fermions and quantum gases. I will then provide an outlook to the future and discuss how in the short term analog quantum simulators can help tackle problems for which no efficient simulation algorithms exist and how in the longer term quantum computers can be used to solve many of the still open questions in the field. I will finally connect to the topic of the remainder of this symposium by touching on how the design of new topological materials will help in the construction of these quantum computers.
NASA Astrophysics Data System (ADS)
Popkov, Vladislav; Salerno, Mario
2013-06-01
In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.
NASA Astrophysics Data System (ADS)
Popkov, Vladislav; Salerno, Mario
2012-11-01
In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Rényi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.
Quantum versus mean-field collapse in a many-body system
NASA Astrophysics Data System (ADS)
Astrakharchik, G. E.; Malomed, B. A.
2015-10-01
The recent analysis, based on the mean-field approximation (MFA), has predicted that the critical quantum collapse of the bosonic wave function, pulled to the center by the inverse-square potential in the three-dimensional space, is suppressed by the repulsive cubic nonlinearity in the bosonic gas, the collapsing ground state being replaced by a regular one. We demonstrate that a similar stabilization acts in a quantum many-body system, beyond the MFA. While the collapse remains possible, repulsive two-particle interactions give rise to a metastable gaseous state, which is separated by a potential barrier from the collapsing regime. The stability of this state improves with the increase of the number of particles. The results are produced by calculations of the variational energy, with the help of the Monte Carlo method.
The Interplay of Localization and Interactions in Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Iyer, Shankar
Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g., disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important. The first is the so-called "dirty" or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder. The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting ("ergodic") phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
NASA Astrophysics Data System (ADS)
Fusco, L.; Pigeon, S.; Apollaro, T. J. G.; Xuereb, A.; Mazzola, L.; Campisi, M.; Ferraro, A.; Paternostro, M.; De Chiara, G.
2014-07-01
We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.
Seniority in quantum many-body systems. I. Identical particles in a single shell
Van Isacker, P.
2014-10-15
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of partial conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions. - Highlights: • Unified derivation of conditions for the total and partial conservation of seniority. • General analysis of the partial conservation of seniority in boson systems. • Why partial conservation of seniority is crucial for seniority isomers in nuclei. • The effect of partial conservation of seniority on one-nucleon transfer intensities.
Exploiting Quantum Parallelism to Simulate Quantum Random Many-Body Systems
Paredes, B.; Cirac, J.I.; Verstraete, F.
2005-09-30
We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an auxiliary system. We show how our algorithm allows for the efficient simulation of dynamics of quantum random spin chains with known numerical methods. We propose an experimental realization based on atoms in optical lattices in which disorder could be simulated in parallel and in a controlled way through the interaction with another atomic species.
Spectrum of quantum transfer matrices via classical many-body systems
NASA Astrophysics Data System (ADS)
Gorsky, A.; Zabrodin, A.; Zotov, A.
2014-01-01
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous n -invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N -body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N -dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the n Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.
Goldmann, E. Jahnke, F.; Lorke, M.; Frauenheim, T.
2014-06-16
The saturation behaviour of optical gain with increasing excitation density is an important factor for laser device performance. For active materials based on self-organized InGaAs/GaAs quantum dots, we study the interplay between structural properties of the quantum dots and many-body effects of excited carriers in the optical properties via a combination of tight-binding and quantum-kinetic calculations. We identify regimes where either phase-space filling or excitation-induced dephasing dominates the saturation behavior of the optical gain. The latter can lead to the emergence of a negative differential material gain.
NASA Astrophysics Data System (ADS)
Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji
2016-04-01
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.
Variational Jastrow coupled-cluster theory of quantum many-body systems
NASA Astrophysics Data System (ADS)
Xian, Y.
2008-04-01
We study many-body correlations in the ground state of a general quantum system of bosons or fermions by including an additional Jastrow function in our recently proposed variational coupled-cluster method. Our approach combines the advantages of state-dependent correlations in the coupled-cluster theory and of the strong, short-ranged correlations of the Jastrow function. We apply a generalized linked-cluster expansion for the Jastrow wave function and provide a detailed analysis for practical evaluation of the Hamiltonian expectation value as an energy functional of the Jastrow function and the bare density-distribution functions introduced and calculated in our earlier publications; a simple, first-order energy functional is derived and detailed formulas for the higher-order contributions are provided. Our energy functional does not suffer the divergence as most coupled-cluster calculations often do when applying to Hamiltonians with hardcore potentials. We also discuss possible applications of our technique, including applications to strongly correlated fermion systems.
Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System
NASA Astrophysics Data System (ADS)
Smith, Jacob; Senko, Crystal; Richerme, Phil; Lee, Aaron; Campbell, Wes; Monroe, Chris
2014-05-01
Trapped-ion quantum simulators are a promising candidate for exploring quantum-many-body physics, such as quantum magnetism, that are difficult to examine in condensed-matter experiments or using classical simulation. We demonstrate a coherent imaging spectroscopic technique to validate a quantum simulation. In this work, we study fully-connected transverse Ising models with a chain of up to 18 171Yb+ ions. Here, We resolve the state of each spin by collecting the spin-dependent fluorescence on a camera in order to map the complete energy spectrum and fully characterize the spin-spin couplings, while also engineering entangled states and measuring the critical gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators. This work is supported by grants from the U.S. Army Research Office with funding from the DARPA OLE program, IARPA, and the MURI program; and the NSF Physics Frontier Center at JQI.
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus
2015-05-01
Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.
NASA Astrophysics Data System (ADS)
Deckman, Jason
The following dissertation is an account of my research in the Mandelshtam group at UC Irvine beginning in the Fall of 2006 and ending in the Summer of 2011. My general area of study falls within the realm of equilibrium quantum statistical mechanics, a discipline which attempts to relate molecular-scale properties to time averaged, macroscopic observables. The major tools used herein are the Variational Gaussian Wavepacket (VGW) approximation for quantum calculations, and Monte-Carlo methods, particularly parallel tempering, for global optimization and the prediction of equilibrium thermodynamic properties. Much of my work used these two methods to model both small and bulk systems at equilibrium where quantum effects are significant. All the systems considered are characterized by inter-molecular van der Waals forces, which are weak but significant electrostatic attractions between atoms and molecules and posses a 1/r6 dependence. The research herein begins at the microscopic level, starting with Lennard-Jones (LJ) clusters, then later shifts to the macroscopic for a study involving bulk para-hydrogen. For the LJ clusters the structural transitions induced by a changing deBoer parameter, Λ, a measure of quantum delocalization of the constituent particles, are investigated over a range of cluster sizes, N. From the data a "phase" diagram as a function of Λ and N is constructed, which depicts the structural motifs favored at different size and quantum parameter. Comparisons of the "quantum induced" structural transitions depicted in the latter are also made with temperature induced transitions and those caused by varying the range of the Morse potential. Following this, the structural properties of binary para-Hydrogen/ ortho-Deuterium clusters are investigated using the VGW approximation and Monte-Carlo methods within the GMIN framework. The latter uses the "Basin-Hopping" algorithm, which simplifies the potential energy landscape, and coupled with the VGW approximation, an efficient and viable method for predicting equilibrium quantum mechanical properties is demonstrated. In the next chapter my contribution to the numerical implementation of the Thermal Gaussian Molecular Dynamics (TGMD) method is discussed. Within TGMD, a mapping of a quantum system to a classical is performed by means of an effective Hamiltonian, H eff, which is computed within the VGW framework. Using the classical dynamical equations of motion with Heff, the properties of a quantum system can be modeled within a classical framework. After this, the bulk system of fluid para-Hydrogen is investigated using the VGW in the NPT ensemble in an attempt to derive the thermodynamic properties at the phase transition and construct the equation of state. The dissertation then concludes with a discussion on the adaptation of the VGW methodology to any molecular system.
NASA Astrophysics Data System (ADS)
Mazzucchi, Gabriel; Kozlowski, Wojciech; Caballero-Benitez, Santiago F.; Elliott, Thomas J.; Mekhov, Igor B.
2016-02-01
Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Coupling these systems to quantized light leads to a plethora of new phenomena and has opened up a new field of study. Here we introduce an unusual additional source of competition in a many-body strongly correlated system: We prove that quantum backaction of global measurement is able to efficiently compete with intrinsic short-range dynamics of an atomic system. The competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period without the need of single site addressing. In coherence with a general physical concept, where new competitions typically lead to new phenomena, we demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, long-range entanglement, and correlated tunneling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect. We demonstrate both the breakup and protection of strongly interacting fermion pairs by measurement. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems.
NASA Astrophysics Data System (ADS)
Olmos, Beatriz; Lesanovsky, Igor; Garrahan, Juan P.
2014-10-01
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.
NASA Astrophysics Data System (ADS)
Lavalle, Catia; Rigol, Marcos; Muramatsu, Alejandro
2005-08-01
The cover picture of the current issue, taken from the Feature Article [1], depicts the evolution of local density (a) and its quantum fluctuations (b) in trapped fermions on one-dimensional optical lattices. As the number of fermions in the trap is increased, figure (a) shows the formation of a Mott-insulating plateau (local density equal to one) whereas the quantum fluctuations - see figure (b) - are strongly suppressed, but nonzero. For a larger number of fermions new insulating plateaus appear (this time with local density equal to two), but no density fluctuations. Regions with non-constant density are metallic and exhibit large quantum fluctuations of the density.The first author Catia Lavalle is a Postdoc at the University of Stuttgart. She works in the field of strongly correlated quantum systems by means of Quantum Monte Carlo methods (QMC). While working on her PhD thesis at the University of Stuttgart, she developed a new QMC technique that allows to study dynamical properties of the t-J model.
Simulation of Quantum Many-Body Systems with Strings of Operators and MonteCarlo Tensor Contractions
NASA Astrophysics Data System (ADS)
Schuch, Norbert; Wolf, Michael M.; Verstraete, Frank; Cirac, J. Ignacio
2008-02-01
We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
NASA Astrophysics Data System (ADS)
Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco
2015-11-01
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Hernández-Rojas, Javier; Calvo, Florent; Noya, Eva Gonzalez
2015-03-10
The semiclassical method of quantum thermal baths by colored noise thermostats has been used to simulate various atomic systems in the molecular and bulk limits, at finite temperature and in moderately to strongly anharmonic regimes. In all cases, the method performs relatively well against alternative approaches in predicting correct energetic properties, including in the presence of phase changes, provided that vibrational delocalization is not too strong-neon appearing already as an upper limiting case. In contrast, the dynamical behavior inferred from global indicators such as the root-mean-square bond length fluctuation index or the vibrational spectrum reveals more marked differences caused by zero-point energy leakage, except in the case of isolated molecules with well separated vibrational modes. To correct for such deficiencies and reduce the undesired transfer among modes, empirical modifications of the noise power spectral density were attempted to better describe thermal equilibrium but still failed when used as semiclassical preparation for microcanonical trajectories. PMID:26579740
Controlling the Dynamics of an Open Many-Body Quantum System with Localized Dissipation
NASA Astrophysics Data System (ADS)
Barontini, G.; Labouvie, R.; Stubenrauch, F.; Vogler, A.; Guarrera, V.; Ott, H.
2013-01-01
We experimentally investigate the action of a localized dissipative potential on a macroscopic matter wave, which we implement by shining an electron beam on an atomic Bose-Einstein condensate (BEC). We measure the losses induced by the dissipative potential as a function of the dissipation strength observing a paradoxical behavior when the strength of the dissipation exceeds a critical limit: for an increase of the dissipation rate the number of atoms lost from the BEC becomes lower. We repeat the experiment for different parameters of the electron beam and we compare our results with a simple theoretical model, finding excellent agreement. By monitoring the dynamics induced by the dissipative defect we identify the mechanisms which are responsible for the observed paradoxical behavior. We finally demonstrate the link between our dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect. Because of the high degree of control on every parameter, our system is a promising candidate for the engineering of fully governable open quantum systems.
NASA Astrophysics Data System (ADS)
Eichler, C.; Mlynek, J.; Butscher, J.; Kurpiers, P.; Hammerer, K.; Osborne, T. J.; Wallraff, A.
2015-10-01
Improving the understanding of strongly correlated quantum many-body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research, and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate, and experimentally probe the properties of such systems. In this work, we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product statesa class of states that has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics system, we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to a variety of models including those involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.
Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States
NASA Astrophysics Data System (ADS)
Xie, Z. Y.; Chen, J.; Yu, J. F.; Kong, X.; Normand, B.; Xiang, T.
2014-01-01
We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.
Tensor Renormalization of Quantum Many-Body Systems using Projected Entangled Simplex States
NASA Astrophysics Data System (ADS)
Xiang, T.; Xie, Z. Y.; Chen, J.; Yu, J. F.; Kong, X.; Normand, B.
2014-03-01
We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states (PEPS) to a simplex. PESS are an exact representation of the simplex solid states and provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain an accurate result for the ground-state energy, e0 = - 0 . 4388(1) J , which sets the lowest upper bound yet achieved for this quantity.
Ultracold Quantum Gases:. Experiments with Many-Body Systems in Controlled Environments
NASA Astrophysics Data System (ADS)
Krüger, Peter
2013-02-01
Experiments with ultracold gases have assumed a significant role in atomic physics with direct and major relevance in condensed matter and many other areas of physics. We give a few examples of studies that have been carried out with these systems since the first production of a Bose-Einstein condensate in a dilute atomic vapour in 1995. We discuss in particular early studies of the formation and growth of condensates, excitations of Bose-Einstein condensates, and more recent investigations of strongly correlated systems, arising in optical lattices, near Feshbach resonances, and in restricted geometries of effiective low dimensionality. The understanding of such experiments requires advanced finitetemperature non-equilibrium theories, the discussion of which forms the basis for this book.
Tanaka, Toshiaki
2007-10-15
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed algebra. Within our formulation, we show generically that every parasupersymmetric quantum system of order p consists of N-fold supersymmetric pairs with N{<=}p and thus has weak quasi-solvability and isospectral property. We also propose a new type of non-linear supersymmetries, called quasi-parasupersymmetry, which is less restrictive than parasupersymmetry and is different from N-fold supersymmetry even in one-body systems though the conserved charges are represented by higher-order linear differential operators. To illustrate how our formulation works, we construct second-order parafermionic algebra and three simple examples of parasupersymmetric quantum systems of order 2, one is essentially equivalent to the one-body Rubakov-Spiridonov type and the others are two-body systems in which two supersymmetries are folded. In particular, we show that the first model admits a generalized 2-fold superalgebra.
Sciolla, Bruno; Poletti, Dario; Kollath, Corinna
2015-05-01
We use two-time correlation functions to study the complex dynamics of dissipative many-body quantum systems. In order to measure, understand, and categorize these correlations we extend the framework of the adiabatic elimination method. We show that, for the same parameters and times, two-time correlations can display two distinct behaviors depending on the observable considered: a fast exponential decay or a much slower dynamics. We exemplify these findings by studying strongly interacting bosons in a double well subjected to phase noise. While the single-particle correlations decay exponentially fast with time, the density-density correlations display slow aging dynamics. We also show that this slow relaxation regime is robust against particle losses. Additionally, we use the developed framework to show that the dynamic properties of dissipatively engineered states can be drastically different from their Hamiltonian counterparts. PMID:25978211
NASA Astrophysics Data System (ADS)
Sciolla, Bruno; Poletti, Dario; Kollath, Corinna
2015-05-01
We use two-time correlation functions to study the complex dynamics of dissipative many-body quantum systems. In order to measure, understand, and categorize these correlations we extend the framework of the adiabatic elimination method. We show that, for the same parameters and times, two-time correlations can display two distinct behaviors depending on the observable considered: a fast exponential decay or a much slower dynamics. We exemplify these findings by studying strongly interacting bosons in a double well subjected to phase noise. While the single-particle correlations decay exponentially fast with time, the density-density correlations display slow aging dynamics. We also show that this slow relaxation regime is robust against particle losses. Additionally, we use the developed framework to show that the dynamic properties of dissipatively engineered states can be drastically different from their Hamiltonian counterparts.
Many-body localization in the quantum random energy model
NASA Astrophysics Data System (ADS)
Laumann, Chris; Pal, Arijeet
2014-03-01
The quantum random energy model is a canonical toy model for a quantum spin glass with a well known phase diagram. We show that the model exhibits a many-body localization-delocalization transition at finite energy density which significantly alters the interpretation of the statistical ``frozen'' phase at lower temperature in isolated quantum systems. The transition manifests in many-body level statistics as well as the long time dynamics of on-site observables. CRL thanks the Perimeter Institute for hospitality and support.
NASA Astrophysics Data System (ADS)
Doyeux, Pierre; Leggio, Bruno; Messina, Riccardo; Antezza, Mauro
2016-02-01
We study the functioning of a three-level thermal machine when acting on a many-qubit system, the entire system being placed in an electromagnetic field in a stationary out-of-thermal-equilibrium configuration. This realistic setup stands between the two so-far-explored cases of single-qubit and macroscopic object targets, providing information on the scaling with system size of purely quantum properties in thermodynamic contexts. We show that, thanks to the presence of robust correlations among the qubits induced by the field, thermodynamic tasks can be delivered by the machine both locally to each qubit and collectively to the many-qubit system: This allows a task to be delivered also on systems much bigger than the machine size.
Lao, Ka Un; Herbert, John M
2015-01-15
We present an overview of "XSAPT", a family of quantum chemistry methods for noncovalent interactions. These methods combine an efficient, iterative, monomer-based approach to computing many-body polarization interactions with a two-body version of symmetry-adapted perturbation theory (SAPT). The result is an efficient method for computing accurate intermolecular interaction energies in large noncovalent assemblies such as molecular and ionic clusters, molecular crystals, clathrates, or protein-ligand complexes. As in traditional SAPT, the XSAPT energy is decomposable into physically meaningful components. Dispersion interactions are problematic in traditional low-order SAPT, and two new approaches are introduced here in an attempt to improve this situation: (1) third-generation empirical atom-atom dispersion potentials, and (2) an empirically scaled version of second-order SAPT dispersion. Comparison to high-level ab initio benchmarks for dimers, water clusters, halide-water clusters, a methane clathrate hydrate, and a DNA intercalation complex illustrate both the accuracy of XSAPT-based methods as well as their limitations. The computational cost of XSAPT scales as O(N(3))-O(N(5)) with respect to monomer size, N, depending upon the particular version that is employed, but the accuracy is typically superior to alternative ab initio methods with similar scaling. Moreover, the monomer-based nature of XSAPT calculations makes them trivially parallelizable, such that wall times scale linearly with respect to the number of monomer units. XSAPT-based methods thus open the door to both qualitative and quantitative studies of noncovalent interactions in clusters, biomolecules, and condensed-phase systems. PMID:25408114
Many-body localization in dipolar systems.
Yao, N Y; Laumann, C R; Gopalakrishnan, S; Knap, M; Müller, M; Demler, E A; Lukin, M D
2014-12-12
Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities. PMID:25541771
Many-Body Localization in Dipolar Systems
NASA Astrophysics Data System (ADS)
Yao, N. Y.; Laumann, C. R.; Gopalakrishnan, S.; Knap, M.; Mller, M.; Demler, E. A.; Lukin, M. D.
2014-12-01
Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities.
Quantum many-body interactions in digital oxide superlattices.
Monkman, Eric J; Adamo, Carolina; Mundy, Julia A; Shai, Daniel E; Harter, John W; Shen, Dawei; Burganov, Bulat; Muller, David A; Schlom, Darrell G; Shen, Kyle M
2012-10-01
Controlling the electronic properties of interfaces has enormous scientific and technological implications and has been recently extended from semiconductors to complex oxides that host emergent ground states not present in the parent materials. These oxide interfaces present a fundamentally new opportunity where, instead of conventional bandgap engineering, the electronic and magnetic properties can be optimized by engineering quantum many-body interactions. We use an integrated oxide molecular-beam epitaxy and angle-resolved photoemission spectroscopy system to synthesize and investigate the electronic structure of superlattices of the Mott insulator LaMnO(3) and the band insulator SrMnO(3). By digitally varying the separation between interfaces in (LaMnO(3))(2n)/(SrMnO(3))(n) superlattices with atomic-layer precision, we demonstrate that quantum many-body interactions are enhanced, driving the electronic states from a ferromagnetic polaronic metal to a pseudogapped insulating ground state. This work demonstrates how many-body interactions can be engineered at correlated oxide interfaces, an important prerequisite to exploiting such effects in novel electronics. PMID:22902897
Decoherence of many-body systems due to many-body interactions
Carle, T.; Kraus, B.; Briegel, H. J.
2011-07-15
We study a spin-gas model, where N{sub S} system qubits are interacting with N{sub B} bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decoherence induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between bath qubits that are coupled to different individual system qubits and compare Markovian with non-Markovian scenarios. We derive a useful canonical form of a completely positive map that describes a class of system environment interactions with a finite size of environment correlations. As examples we consider specific quantum many-body states and investigate their evolution under different decoherence models. As a complementary investigation, we study how the coupling to the environment can be employed to generate a desired multipartite state.
Quantum power functional theory for many-body dynamics.
Schmidt, Matthias
2015-11-01
We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems. PMID:26547159
Exploring flocking via quantum many-body physics techniques
NASA Astrophysics Data System (ADS)
Souslov, Anton; Loewe, Benjamin; Goldbart, Paul M.
2015-03-01
Flocking refers to the spontaneous breaking of spatial isotropy and time-reversal symmetries in collections of bodies such as birds, fish, locusts, bacteria, and artificial active systems. The transport of matter along biopolymers using molecular motors also involves the breaking of these symmetries, which in some cases are known to be broken explicitly. We study these classical nonequilibrium symmetry-breaking phenomena by means of models of many strongly interacting particles that hop on a periodic lattice. We employ a mapping between the classical and quantum dynamics of many-body systems, combined with tools from many-body theory. In particular, we examine the formation and properties of nematic and polar order in low-dimensional, strongly-interacting active systems using techniques familiar from fermionic systems, such as self-consistent field theory and bosonization. Thus, we find that classical active systems can exhibit analogs of quantum phenomena such as spin-orbit coupling, magnetism, and superconductivity. The models we study connect the physics of asymmetric exclusion processes to the spontaneous emergence of transport and flow, and also provide a soluble cousin of Vicsek's model system of self-propelled particles.
Collision Microscope to Study Many-Body Quantum Entanglement
NASA Astrophysics Data System (ADS)
Price, Craig; Liu, Qi; Gemelke, Nathan
2014-05-01
Quantum entanglement over long length scales is present in both quantum critical and quantum ordered many-body systems and can often be used as a fingerprint for underlying dynamics or ground-state structure. Limited quantum measurement and thermal back-action via controlled collisions of cold atoms and subsequent optical detection can be used to probe long-range entanglement. Entanglement Entropy has recently arisen as a quantitative vehicle to describe entanglement in thermodynamic systems, and its scaling with area can reveal detailed character of the system. We present progress in constructing an apparatus to experimentally extract Entanglement Entropy through pair-wise entanglement of cold fermionic potassium and bosonic cesium gases. The measurement will be made by translating localized probe atoms through a portion of a strongly entangled sample, then recording the heating effect of back-action after optical detection of probe atoms. To do so, precise independent control over the atoms will be maintained in a bichromatic lattice formed with a monolithic, common-mode optical setup imbedded in a quantum gas microscope. Other applications are discussed, including cooling of a Mott-Insulator and study of non-equilibrium quantum systems.
EDITORIAL: Focus on Quantum Information and Many-Body Theory
NASA Astrophysics Data System (ADS)
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac and F Verstraete SIMULATION AND DYNAMICS A quantum differentiation of k-SAT instances B Tamir and G Ortiz Classical Ising model test for quantum circuits Joseph Geraci and Daniel A Lidar Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain S R Clark, J Prior, M J Hartmann, D Jaksch and M B Plenio Exact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition Tomaž Prosen and Bojan Žunkovič Quantum kinetic Ising models R Augusiak, F M Cucchietti, F Haake and M Lewenstein ENTANGLEMENT AND SPECTRAL PROPERTIES Ground states of unfrustrated spin Hamiltonians satisfy an area law Niel de Beaudrap, Tobias J Osborne and Jens Eisert Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group W Münder, A Weichselbaum, A Holzner, Jan von Delft and C L Henley The invariant-comb approach and its relation to the balancedness of multipartite entangled states Andreas Osterloh and Jens Siewert Entanglement scaling of fractional quantum Hall states through geometric deformations Andreas M Läuchli, Emil J Bergholtz and Masudul Haque Entanglement versus gap for one-dimensional spin systems Daniel Gottesman and M B Hastings Entanglement spectra of critical and near-critical systems in one dimension F Pollmann and J E Moore Macroscopic bound entanglement in thermal graph states D Cavalcanti, L Aolita, A Ferraro, A García-Saez and A Acín Entanglement at the quantum phase transition in a harmonic lattice Elisabeth Rieper, Janet Anders and Vlatko Vedral Multipartite entanglement and frustration P Facchi, G Florio, U Marzolino, G Parisi and S Pascazio Entropic uncertainty relations—a survey Stephanie Wehner and Andreas Winter Entanglement in a spin system with inverse square statistical interaction D Giuliano, A Sindona, G Falcone, F Plastina and L Amico APPLICATIONS Time-dependent currents of one-dimensional bosons in an optical lattice J Schachenmayer, G Pupillo and A J Daley Implementing quantum gates using the ferromagnetic spin-J XXZ chain with kink boundary conditions Tom Michoel, Jaideep Mulherkar and Bruno Nachtergaele Long-distance entanglement in many-body atomic and optical systems Salvatore M Giampaolo and Fabrizio Illuminati QUANTUM MEMORIES AND TOPOLOGICAL ORDER Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes Stefano Chesi, Daniel Loss, Sergey Bravyi and Barbara M Terhal Topological color codes and two-body quantum lattice Hamiltonians M Kargarian, H Bombin and M A Martin-Delgado RENORMALIZATION Local renormalization method for random systems O Gittsovich, R Hübener, E Rico and H J Briegel
Analyzing Many-Body Localization with a Quantum Computer
NASA Astrophysics Data System (ADS)
Bauer, Bela; Nayak, Chetan
2014-10-01
Many-body localization, the persistence against electron-electron interactions of the localization of states with nonzero excitation energy density, poses a challenge to current methods of theoretical and numerical analyses. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.
Quantum quenches, thermalization, and many-body localization
NASA Astrophysics Data System (ADS)
Canovi, Elena; Rossini, Davide; Fazio, Rosario; Santoro, Giuseppe E.; Silva, Alessandro
2011-03-01
We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the system’s eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space.
Mirages and many-body effects in quantum corrals
NASA Astrophysics Data System (ADS)
Aligia, A. A.; Lobos, A. M.
2005-04-01
In an experiment on quantum mirages, confinement of surface states in an elliptical corral has been used to project the Kondo effect from one focus where a magnetic impurity was placed to the other, empty, focus. The signature of the Kondo effect is seen as a Fano antiresonance in scanning tunnelling spectroscopy. This experiment combines the many-body physics of the Kondo effect with the subtle effects of confinement. In this work we review the essential physics of the quantum mirage experiment, and present new calculations involving other geometries and more than one impurity in the corral, which should be relevant for other experiments that are being made, and to discern the relative importance of the hybridization of the impurity with surface (Vs) and bulk (Vb) states. The intensity of the mirage imposes a lower bound on Vs/Vb which we estimate. Our emphasis is on the main physical ingredients of the phenomenon and the many-body aspects, like the dependence of the observed differential conductance on the geometry, which cannot be calculated with alternative one-body theories. The system is described with an Anderson impurity model solved using complementary approaches: theory of perturbation in the Coulomb repulsion U, slave bosons in the mean field and exact diagonalization plus embedding.
Quantum quenches in the many-body localized phase
NASA Astrophysics Data System (ADS)
Serbyn, Maksym; Papić, Z.; Abanin, D. A.
2014-11-01
Many-body localized (MBL) systems are characterized by the absence of transport and thermalization and, therefore, cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behavior of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly nonthermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behavior distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached) and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultracold atoms in disordered optical lattices, and the behavior of local observables provides a direct experimental signature of many-body localization.
On Many-Body Localization for Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-06-01
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
On Many-Body Localization for Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-04-01
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
Many-Body Localization in Simulation of Fermionic Systems
NASA Astrophysics Data System (ADS)
Chapman, Adrian; Miyake, Akimasa
In the widely-known setting of Anderson localization, noninteracting particles in a disordered potential remain confined to their initial positions, even in the infinite-time limit. Many-body localization (MBL) is the extension of this phenomenon to the regime in which the particles are weakly interacting. Recent results have demonstrated examples of many-body localized systems whose evolution may be approximately simulated classically as a result of this confinement to within a ``logarithmic light cone.'' Here we attempt to turn the question on its head and ask whether MBL could be used as a means of simulating quantum computations that na?vely appear difficult. We focus on one-dimensional fermionic systems, which admit techniques for classical simulation in the noninteracting case but are universal for quantum computation upon the introduction of interactions. I will describe some recent progress in this direction as well as discuss possible future endeavours.
Entanglement replication in driven dissipative many-body systems.
Zippilli, S; Paternostro, M; Adesso, G; Illuminati, F
2013-01-25
We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks. PMID:25166146
NASA Astrophysics Data System (ADS)
Chin, Cheng
2011-05-01
Recent cold atom researches are reaching out far beyond the realm that was conventionally viewed as atomic physics. Many long standing issues in other physics disciplines or in Gedanken-experiments are nowadays common targets of cold atom physicists. Two prominent examples will be discussed in this talk: BEC-BCS crossover and Efimov physics. Here, cold atoms are employed to emulate electrons in superconductors, and nucleons in nuclear reactions, respectively. The ability to emulate exotic or thought systems using cold atoms stems from the precisely determined, simple, and tunable interaction properties of cold atoms. New experimental tools have also been devised toward an ultimate goal: a complete control and a complete characterization of a few- or many-body quantum system. We are tantalizingly close to this major milestone, and will soon open new venues to explore new quantum phenomena that may (or may not!) exist in scientists' dreams.
Many-body energy localization transition in periodically driven systems
D’Alessio, Luca; Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 ; Polkovnikov, Anatoli
2013-06-15
According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space. -- Highlights: •A dynamical localization transition in periodically driven ergodic systems is found. •This phenomenon is reminiscent of many-body localization in energy space. •Our results are valid for classical and quantum systems in the thermodynamic limit. •At critical frequency, the short time expansion for the evolution operator breaks down. •The transition is associated to a divergent time scale.
Many-Body Effects in Quantum-Well Intersubband Transitions
NASA Technical Reports Server (NTRS)
Li, Jian-Zhong; Ning, Cun-Zheng
2003-01-01
Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (Qw) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons (ISPs). The oscillator strength of intersubband transitions (ISBTs) strongly varies with QW parameters and electron density because of this coupling. We have developed a set of kinetic equations, termed the intersubband semiconductor Bloch equations (ISBEs), from density matrix theory with the Hartree-Fock approximation, that enables a consistent description of these many-body effects. Using the ISBEs for a two-conduction-subband model, various many-body effects in intersubband transitions are studied in this work. We find interesting spectral changes of intersubband absorption coefficient due to interplay of the Fermi-edge singularity, subband renormalization, intersubband plasmon oscillation, and nonparabolicity of bandstructure. Our results uncover a new perspective for ISBTs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBT line shape.
NASA Astrophysics Data System (ADS)
Babadi, Mehrtash; Demler, Eugene; Knap, Michael
2015-10-01
We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-1 /2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1 /N expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild et al., Phys. Rev. Lett. 113, 147205 (2014), 10.1103/PhysRevLett.113.147205].
A Many Body Eigenvalue Problem for Quantum Computation
NASA Astrophysics Data System (ADS)
Hershfield, Selman
2008-03-01
A one dimensional many body Hamiltonian is presented whose eigenvalues are related to the order of GN. This is the same order of GN used to decode the RSA algorithm. For some values of N the Hamiltonian is a noninteracting fermion problem. For other values of N the Hamiltonian is a quantum impurity problem with fermions interacting with a spin-like object. However, the generic case has fermions or spins interacting with higher order interactions beyond two body interactions. Because this is a mapping between two different classes of problems, one of interest in quantum computing and the other a more traditional condensed matter physics Hamiltonian, we will show (i) how knowledge of the order of GN can be used to solve some novel one dimensional strongly correlated problems and (ii) how numerical techniques, particularly for quantum impurity limit, can be used to find the order of GN.
Computational nuclear quantum many-body problem: The UNEDF project
Fann, George I
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Critical quasienergy states in driven many-body systems
NASA Astrophysics Data System (ADS)
Bastidas Valencia, Victor Manuel; Engelhardt, Georg; Perez-Fernandez, Pedro; Vogl, Malte; Brandes, Tobias
2015-03-01
A quantum phase transition (QPT) is characterized by non-analyticities of ground-state properties at the critical points. Recently it has been shown that quantum criticality emerges also in excited states of the system, which is referred to as an excited-state quantum phase transition (ESQPT). This kind of quantum criticality is intimately related to a level clustering at critical energies, which results in a logarithmic singularity in the density of states. Most of the previous studies on quantum criticality in excited states have been focused on time independent systems. Here we study spectral singularities that appear in periodically-driven many-body systems and show how the external control allows one to engineer geometrical features of the quasienergy landscape. In particular, we study singularities in the quasienergy spectrum of a fully-connected network consisting of two-level systems with time-dependent interactions. We discuss the characteristic signatures of these singularities in observables like the magnetization, which should be measurable with current technology. The authors gratefully acknowledge financial support by the DFG via grants BRA 1528/7, BRA 1528/8, SFB 910 (V.M.B., T.B.), the Spanish Ministerio de Ciencia e Innovacion (Grants No. FIS2011-28738-C02-01) and Junta de Andalucia (Grants No. FQM160).
Many-body localization and quantum ergodicity in disordered long-range Ising models
NASA Astrophysics Data System (ADS)
Hauke, Philipp; Heyl, Markus
2015-10-01
Ergodicity in quantum many-body systems is—despite its fundamental importance—still an open problem. Many-body localization provides a general framework for quantum ergodicity and may therefore offer important insights. However, the characterization of many-body localization through simple observables is a difficult task. In this article, we introduce a measure for distances in Hilbert space for spin-1/2 systems that can be interpreted as a generalization of the Anderson localization length to many-body Hilbert space. We show that this many-body localization length is equivalent to a simple local observable in real space, which can be measured in experiments of superconducting qubits, polar molecules, Rydberg atoms, and trapped ions. By using the many-body localization length and a necessary criterion for ergodicity that it provides, we study many-body localization and quantum ergodicity in power-law-interacting Ising models subject to disorder in a transverse field. Based on the nonequilibrium dynamical renormalization group, numerically exact diagonalization, and an analysis of the statistics of resonances, we find a many-body localized phase at infinite temperature for small power-law exponents. Within the applicability of these methods, we find no indications of a delocalization transition.
Typical fast thermalization processes in closed many-body systems.
Reimann, Peter
2016-01-01
The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium. PMID:26926224
Typical fast thermalization processes in closed many-body systems
NASA Astrophysics Data System (ADS)
Reimann, Peter
2016-03-01
The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium.
Typical fast thermalization processes in closed many-body systems
Reimann, Peter
2016-01-01
The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium. PMID:26926224
Ideal quantum glass transitions: Many-body localization without quenched disorder
Schiulaz, M.; Müller, M.
2014-08-20
We explore the possibility for translationally invariant quantum many-body systems to undergo a dynamical glass transition, at which ergodicity and translational invariance break down spontaneously, driven entirely by quantum effects. In contrast to analogous classical systems, where the existence of such an ideal glass transition remains a controversial issue, a genuine phase transition is predicted in the quantum regime. This ideal quantum glass transition can be regarded as a many-body localization transition due to self-generated disorder. Despite their lack of thermalization, these disorder-free quantum glasses do not possess an extensive set of local conserved operators, unlike what is conjectured for many-body localized systems with strong quenched disorder.
Entanglement between noncomplementary parts of many-body systems
NASA Astrophysics Data System (ADS)
Wichterich, H. C.
This thesis investigates the properties of entanglement in strongly correlated quantum systems, more specifically that between regions of a many-body system which may be separated spatially giving rise to a part of the system which is disregarded. The focus of the first part of this thesis is the response of a collection of spins, arranged on a one dimensional lattice, to a global quench, i.e. a rapid change in the interaction characteristics. Such a quench is seen to produce a significant amount of entanglement between distant spins. The robustness of the scheme towards random disorder is detailed and it is shown that the entanglement is sufficiently high to be distilled into almost pure Bell pairs. In a similar model system, it is explored how a von Neumann measurement with post-selection (i.e., discarding certain measurements based on the outcome) performed locally on two possibly well separated regions of spins, may give rise to a pure and entangled state of these regions, assuming the system is in its ground state. Later chapters are concerned with entanglement between noncomplementary groups of spins at quantum critical points, a situation where at zero temperature quantum fluctuations become pronounced. For spin chain models it is observed that this entanglement (as measured by negativity) assumes a finite value depending only on the ratio of the size of the regions to their separation and is further seen to be universal, i.e. independent of the microscopic details of the interaction. Universality of this form of entanglement is finally explored in a collective spin model. By casting the problem into the language of a few bosonic modes a closed form expression for the negativity in the thermodynamic limit for the entire phase diagram of the model is derived. At the quantum critical point this measure is explicitly universal in the aforementioned sense.
Preparation of many-body states for quantum simulation
Ward, Nicholas J.; Kassal, Ivan; Aspuru-Guzik, Alan
2009-05-21
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum states on a lattice in real space. In particular, the present algorithm is able to prepare general pure and mixed many-particle states of any number of particles. It relies on a procedure for converting from a second-quantized state to its first-quantized counterpart. The algorithm is efficient in that it operates in time that is polynomial in all the essential descriptors of the system, the number of particles, the resolution of the lattice, and the inverse of the maximum final error. This scaling holds under the assumption that the wave function to be prepared is bounded or its indefinite integral is known and that the Fock operator of the system is efficiently simulatable.
Preparation of many-body states for quantum simulation.
Ward, Nicholas J; Kassal, Ivan; Aspuru-Guzik, Alán
2009-05-21
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum states on a lattice in real space. In particular, the present algorithm is able to prepare general pure and mixed many-particle states of any number of particles. It relies on a procedure for converting from a second-quantized state to its first-quantized counterpart. The algorithm is efficient in that it operates in time that is polynomial in all the essential descriptors of the system, the number of particles, the resolution of the lattice, and the inverse of the maximum final error. This scaling holds under the assumption that the wave function to be prepared is bounded or its indefinite integral is known and that the Fock operator of the system is efficiently simulatable. PMID:19466819
Exponentially Slow Heating in Periodically Driven Many-Body Systems.
Abanin, Dmitry A; De Roeck, Wojciech; Huveneers, François
2015-12-18
We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including the decay of highly energetic excitations in cold atomic and solid-state systems. PMID:26722939
NASA Astrophysics Data System (ADS)
Sohinger, Vedran
2015-11-01
In this paper, we will obtain a rigorous derivation of the defocusing cubic nonlinear Schr\\"{o}dinger equation on the three-dimensional torus $\\mathbb{T}^3$ from the many-body limit of interacting bosonic systems. This type of result was previously obtained on $\\mathbb{R}^3$ in the work of Erd\\H{o}s, Schlein, and Yau \\cite{ESY2,ESY3,ESY4,ESY5}, and on $\\mathbb{T}^2$ and $\\mathbb{R}^2$ in the work of Kirkpatrick, Schlein, and Staffilani \\cite{KSS}. Our proof relies on an unconditional uniqueness result for the Gross-Pitaevskii hierarchy at the level of regularity $\\alpha=1$, which is proved by using a modification of the techniques from the work of T. Chen, Hainzl, Pavlovi\\'{c} and Seiringer \\cite{ChHaPavSei} to the periodic setting. These techniques are based on the Quantum de Finetti theorem in the formulation of Ammari and Nier \\cite{AmmariNier1,AmmariNier2} and Lewin, Nam, and Rougerie \\cite{LewinNamRougerie}. In order to apply this approach in the periodic setting, we need to recall multilinear estimates obtained by Herr, Tataru, and Tzvetkov \\cite{HTT}. Having proved the unconditional uniqueness result at the level of regularity $\\alpha=1$, we will apply it in order to finish the derivation of the defocusing cubic nonlinear Schr\\"{o}dinger equation on $\\mathbb{T}^3$, which was started in the work of Elgart, Erd\\H{o}s, Schlein, and Yau \\cite{EESY}. In the latter work, the authors obtain all the steps of Spohn's strategy for the derivation of the NLS \\cite{Spohn}, except for the final step of uniqueness. Additional arguments are necessary to show that the objects constructed in \\cite{EESY} satisfy the assumptions of the unconditional uniqueness theorem. Once we achieve this, we are able to prove the derivation result. In particular, we show \\emph{Propagation of Chaos} for the defocusing Gross-Pitaevskii hierarchy on $\\mathbb{T}^3$ for suitably chosen initial data.
Many-body delocalization transition and relaxation in a quantum dot
NASA Astrophysics Data System (ADS)
Gornyi, I. V.; Mirlin, A. D.; Polyakov, D. G.
2016-03-01
We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state," a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.
Coupling Identical one-dimensional Many-Body Localized Systems
NASA Astrophysics Data System (ADS)
Bordia, Pranjal; Lüschen, Henrik P.; Hodgman, Sean S.; Schreiber, Michael; Bloch, Immanuel; Schneider, Ulrich
2016-04-01
We experimentally study the effects of coupling one-dimensional many-body localized systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasirandom on-site disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between many-body localization and Anderson localization. While the noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system.
Quasi Many-Body Localization in Translation Invariant Systems
NASA Astrophysics Data System (ADS)
Yao, Norman; Laumann, Chris; Cirac, J. Ignacio; Lukin, Mikhail; Moore, Joel
2015-03-01
We examine localization phenomena associated with generic, high entropy, states of a translation invariant, one-dimensional spin ladder. At intermediate time scales, we find slow growth of entanglement entropy consistent with the known phenomenology of many-body localization in disordered, interacting systems. At longer times, however, anomalous diffusion sets in, leading to full spin polarization decay on a time-scale exponential in system size. We identify a single length scale which parametrically controls both the eventual spin transport times and the divergence of the susceptibility to spin glass ordering. We dub this pre-thermal dynamical behavior, quasi many-body localization.
Coupling Identical one-dimensional Many-Body Localized Systems.
Bordia, Pranjal; Lüschen, Henrik P; Hodgman, Sean S; Schreiber, Michael; Bloch, Immanuel; Schneider, Ulrich
2016-04-01
We experimentally study the effects of coupling one-dimensional many-body localized systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasirandom on-site disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between many-body localization and Anderson localization. While the noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system. PMID:27104685
Proton - a fascinating relativistic many-body system - remains puzzling
NASA Astrophysics Data System (ADS)
Gao, Haiyan
2015-04-01
Proton, a fundamental building block of visible matter in the universe, is a facinating relativistic many-body system. It is also nature's best laboratory to study strong interaction and quantum chromodynamics, the theory describing it. Despite decades of studies and many discoveries, proton remains puzzling. While the LHC discovery of the Higgs boson validates the mechanism for some fundamental particles to have masses in Standard Model, Higgs is almost irrelevant to the mass of the proton. The European Muon Collaboration discovered in late 1980s that quarks inside the proton contribute only about a quarter to the total spin of the proton. This discovery generated major theoretical and experimental efforts in the last two decades trying to piece together the total spin of the proton. While the proton spin is becoming less puzzling, another new puzzle about proton developed in the last a few years concerning the ``size'' of the proton. The ultrahigh precise value of the proton charge radius determined from muonic hydrogen Lamb shift measurements is 7-8 smaller than values determined from electron-proton scattering experiments and hydrogen Lamb shift measurements. In this talk, I will review these puzzles and the efforts to solve them. This work is supported by the U. S. Department of Energy under Contract No. DE-FG02-03ER41231.
Irreducible many-body correlations in topologically ordered systems
NASA Astrophysics Data System (ADS)
Liu, Yang; Zeng, Bei; Zhou, D. L.
2016-02-01
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation (IMC), the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits IMCs which become reducible when the holes are removed. The appearance of these IMCs then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in external magnetic fields, and show that the topological phase transition is signaled by the IMCs.
Tunable many-body effects in triple quantum dots
NASA Astrophysics Data System (ADS)
Kim, Jihan; Melnikov, Dmitriy V.; Leburton, Jean-Pierre
2009-07-01
Exchange energies and charge densities for a few electrons in electrically tunable triangular and collinear triple quantum dot (TQD) systems are investigated by using the variational Monte Carlo method in the presence of magnetic fields. For N=2 electrons we observe a discontinuity in the J derivative with detuning voltage (dJ/dVT) in triangular triple QDs at B=0T as crossing of the eigenenergy levels leads to abrupt spatial symmetry change in the singlet and the triplet densities (density rotation) and relocalization. For B≠0T , the angular momentum provided to the electrons quenches this effect. The density rotation is absent in the collinear TQD for all magnetic fields as the lowest excited state remains the px state and as such, no change in symmetry is possible. By varying the triangular TQD configuration, we show the discontinuity in dJ/dVT persists for the top angle comprised between ˜20° and ˜70° . For three electrons in the symmetric triangular TQD, the monotonicity of the quadruplet-doublet energy difference from B=0 to 4 T remains intact for decoupled QDs but not for coupled QDs. Finally, addition energy for the triangular TQD system is computed for up to N=3 electrons.
Rotation of Quantum Impurities in the Presence of a Many-Body Environment
NASA Astrophysics Data System (ADS)
Schmidt, Richard; Lemeshko, Mikhail
2015-05-01
We develop a microscopic theory describing a quantum impurity whose rotational degree of freedom is coupled to a many-particle bath. We approach the problem by introducing the concept of an "angulon"—a quantum rotor dressed by a quantum field—and reveal its quasiparticle properties using a combination of variational and diagrammatic techniques. Our theory predicts renormalization of the impurity rotational structure, such as that observed in experiments with molecules in superfluid helium droplets, in terms of a rotational Lamb shift induced by the many-particle environment. Furthermore, we discover a rich many-body-induced fine structure, emerging in rotational spectra due to a redistribution of angular momentum within the quantum many-body system.
Many-body localization in periodically driven systems.
Ponte, Pedro; Papić, Z; Huveneers, François; Abanin, Dmitry A
2015-04-10
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases. PMID:25910094
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
NASA Astrophysics Data System (ADS)
Schachenmayer, J.; Pikovski, A.; Rey, A. M.
2015-01-01
Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.
Adiabatic many-body state preparation and information transfer in quantum dot arrays
NASA Astrophysics Data System (ADS)
Farooq, Umer; Bayat, Abolfazl; Mancini, Stefano; Bose, Sougato
2015-04-01
Quantum simulation of many-body systems are one of the most interesting tasks of quantum technology. Among them is the preparation of a many-body system in its ground state when the vanishing energy gap makes the cooling mechanisms ineffective. Adiabatic theorem, as an alternative to cooling, can be exploited for driving the many-body system to its ground state. In this paper, we study two most common disorders in quantum dot arrays, namely exchange coupling fluctuations and hyperfine interaction, in adiabatic preparation of ground state in such systems. We show that the adiabatic ground-state preparation is highly robust against those disorder effects making it a good analog simulator. Moreover, we also study the adiabatic quantum information transfer, using singlet-triplet states, across a spin chain. In contrast to ground-state preparation the transfer mechanism is highly affected by disorder and in particular, the hyperfine interaction is very destructive for the performance. This suggests that for communication tasks across such arrays adiabatic evolution is not as effective and quantum quenches could be preferable.
A many-body approach to quantum transport dynamics: Initial correlations and memory effects
NASA Astrophysics Data System (ADS)
Myöhänen, P.; Stan, A.; Stefanucci, G.; van Leeuwen, R.
2008-12-01
We study time-dependent quantum transport through a correlated double quantum dot (DQD) model system by means of time propagation of the nonequilibrium many-body Green's function. The theory is an extension of the Kadanoff-Baym approach for finite inhomogeneous systems (Phys. Rev. Lett., 98 (2007) 153004) to open inhomogeneous systems and generalizes the Meir-Wingreen formula to include initial correlations and memory effects. Important features of the theory are 1) the possibility to study the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We calculate time-dependent local currents and densities for different many-body approximations and highlight the role of initial correlations and memory effects on the transient dynamics. Furthermore we show that coherent charge oscillations on the DQD are strongly affected by the confined Coulomb interaction and can be directly related to the local equilibrium spectral density.
Phase-space characterization of complexity in quantum many-body dynamics.
Balachandran, Vinitha; Benenti, Giuliano; Casati, Giulio; Gong, Jiangbin
2010-10-01
We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well-known measure of complexity in classical systems and which is valid for both pure and mixed states in single-particle and many-body systems, takes into account the combined role of chaos and entanglement in the realm of quantum mechanics. The effectiveness of the measure is illustrated in the example of the Ising chain in a homogeneous tilted magnetic field. We provide numerical evidence that the multipartite entanglement generation leads to a linear increase in entropy until saturation in both integrable and chaotic regimes, so that in both cases the number of harmonics of the Wigner function grows exponentially with time. The entropy growth rate can be used to detect quantum phase transitions. The proposed entropy measure can also distinguish between integrable and chaotic many-body dynamics by means of the size of long-term fluctuations which become smaller when quantum chaos sets in. PMID:21230374
Simulation of the many-body dynamical quantum Hall effect in an optical lattice
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Yang, Xu-Chen
2016-05-01
We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations.
Simulation of the many-body dynamical quantum Hall effect in an optical lattice
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Yang, Xu-Chen
2016-02-01
We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations.
Many-Body Green Function of Degenerate Systems
Brouder, Christian; Panati, Gianluca; Stoltz, Gabriel
2009-12-04
A rigorous nonperturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H{sub 0} leading to eigenstates of H{sub 0}+V for degenerate systems. These initial states are eigenstates of P{sub 0}VP{sub 0}, where P{sub 0} is the projection onto a degenerate eigenspace of H{sub 0}. This result is used to give the proper definition of the Green function, the statistical Green function and the nonequilibrium Green function of degenerate systems. The convergence of these Green functions is established.
Exploring dynamics of unstable many-body systems
Volya, Alexander; Zelevinsky, Vladimir
2014-10-15
In this work we acquaint reader with the Continuum Shell Model (CSM), which is a proper theoretical tool for the description of physics of unstable systems. We describe the effective non-Hermitian Hamiltonian of the CSM and concentrate on specific aspects of dynamics using realistic examples. The continuum effects are discussed in the case of weakly bound heavy oxygen isotopes, where inclusion of continuum coupling is necessary to improve the traditional nuclear shell model techniques. Physics of overlapping resonances is illustrated using recent experimental information on {sup 8}B nucleus. In the limit of strong continuum coupling the many-body states restructure relative to continuum leading to a few very broad super-radiant states, while at the same time other states become narrow and nearly decoupled from decay. The recent observations of very broad alpha clustering states in {sup 18}O is one of the most transparent manifestations of super-radiance.
Many-body calculation for charge transport through triangular quantum dot molecules
NASA Astrophysics Data System (ADS)
Chen, Chih-Chieh; Chang, Yia-Chung; Kuo, David M. T.
2015-03-01
We study the many-body effect of electron tunneling through the coupled quantum dots systems in the Coulomb blockade regime. Using the equation of motion method for the non-equilibrium Green's function, we calculate the charge current and conductance of junctions consisting of metallic electrodes and a few quantum dots. Many-particle correlation functions are explicitly solved numerically. Quantum phenomena like quantum interference, Coulomb blockade and spin blockade for the triangular quantum dot molecules are discussed. Our work suggests a new method for the modeling of the mesoscopic transport. This work was supported in part by the Ministry of Science and Technology, Taiwan under Contract Nos. NSC 101-2112-M-001-024-MY3 and NSC 103-2112-M-008-009-MY3.
Real-Time Quantum Dynamics Reveals Complex, Many-Body Interactions in Solvated Nanodroplets.
Oviedo, M Belén; Wong, Bryan M
2016-04-12
Electronic excitations in the liquid phase are surprisingly rich and considerably more complex than either gas-phase or solid-state systems. While the majority of physical and biological processes take place in solvent, our understanding of nonequilibrium excited-state processes in these condensed phase environments remains far from complete. A central and long-standing issue in these solvated environments is the assessment of many-body interactions, particularly when the entire system is out of equilibrium and many quantum states participate in the overall process. Here we present a microscopic picture of solute-solvent electron dynamics and solvatochromic effects, which we uncover using a new real-time quantum dynamics approach for extremely large solvated nanodroplets. In particular, we find that a complex interplay of quantum interactions underlies our observations of solute-solvent effects, and simple macroscopic solvatochromic shifts can even be qualitatively different at the microscopic molecular level in these systems. By treating both the solvent and the solute on the same footing at a quantum-mechanical level, we demonstrate that the electron dynamics in these systems are surprisingly complex, and the emergence of many-body interactions underlies the dynamics in these solvated systems. PMID:26918732
NASA Astrophysics Data System (ADS)
Han, J. E.
2006-03-01
We develope a method of mapping quantum nonequilibrium steady-state to an effective equilibrium system and present an algorithm to calculate electron-transport using an equilibrium technique. A systematic implementation of boundary conditions in steady-state nonequilibrium is made in the statistical operator Ŷ constructed from scattering state operators. We explicitly demonstrate the equivalence of this method to nonequilibrium Green function techniques for a noninteracting quantum dot model. In electron-phonon coupled quantum dot systems, we formulate an algorithm to construct the statistical bias operator Ŷ and perform a full many-body calculation with the quantum Monte Carlo technique. The results coherently demonstrate various transport behaviors such as phonon dephasing, I-V staircase, and phonon-assisted tunneling phenomena. This formulation makes the existing computational quantum many-body techniques applicable to quantum steady-state nonequilibrium problems, which will complement the theories based on the diagrammatic approach.
Spectral statistics of chaotic many-body systems
NASA Astrophysics Data System (ADS)
Dubertrand, Rémy; Müller, Sebastian
2016-03-01
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross-Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose-Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner-Dyson ensembles of random matrix theory. The conditions for Wigner-Dyson statistics involve a gap in the spectrum of the Frobenius-Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.
Dynamics of many-body localization in a translation-invariant quantum glass model
NASA Astrophysics Data System (ADS)
van Horssen, Merlijn; Levi, Emanuele; Garrahan, Juan P.
2015-09-01
We study the real-time dynamics of a translationally invariant quantum spin chain, based on the East kinetically constrained glass model, in search for evidence of many-body localization in the absence of disorder. Numerical simulations indicate a change, controlled by a coupling parameter, from a regime of fast relaxation-corresponding to thermalization-to a regime of very slow relaxation. This slowly relaxing regime is characterized by dynamical features usually associated with nonergodicity and many-body localization (MBL): memory of initial conditions, logarithmic growth of entanglement entropy, and nonexponential decay of time correlators. We show that slow relaxation is a consequence of sensitivity to spatial fluctuations in the initial state. While numerical results and physical considerations indicate that relaxation time scales grow markedly with size, our finite size results are consistent both with an MBL transition, expected to only occur in disordered systems, and with a pronounced quasi-MBL crossover.
Experimental quantum simulations of many-body physics with trapped ions.
Schneider, Ch; Porras, Diego; Schaetz, Tobias
2012-02-01
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems. PMID:22790343
Integrodifferential equation for few- and many-body systems
Fabre de la Ripelle, M.; Fiedeldey, H.; Sofianos, S.A.
1988-07-01
A complete derivation of a new two-variable integrodifferential equation valid for three- and many-boson systems is given here for the first time, and it is shown to be exact if all correlations higher than those of two-body type can be neglected. Its equivalence to the Faddeev equation for three bodies and its applicability to many-body systems are discussed in detail. Three-body forces are included. It is shown that the three- and four-body binding energies obtained by means of this equation are in good agreement with those obtained from the most sophisticated variational, Faddeev, and Faddeev-Yakubovsky calculations. This indicates that our new two-variable integrodifferential equation should also be useful for larger systems, in particular since unlike other methods it does not suffer from the disadvantage of rapidly increasing complexity with A. We also show that a simple adiabatic method for the solution of this equation (and hence also for the Faddeev equation) is quite sufficient, due to the closeness of the upper and lower bounds obtained in this way. Finally we apply the adiabatic method to nuclear three-body scattering and even include the effect of breakup for spin-dependent forces. It is found that asymptotic behavior is reached for a value of the hyperradius of the order of 35 fm.
Dynamical studies of collective behavior of many-body systems
NASA Astrophysics Data System (ADS)
Vergeles, Maxim
This thesis contains the results of the study of the emergent properties of two classes of many-body systems using computational and analytical techniques. (1) The translational and rotational motion of a sphere in a viscous Lennard-Jones liquid has been studied using molecular dynamics simulations. The drag and torque on a sphere in an effectively unbounded fluid are found to agree with continuum hydrodynamics results even when the size of the sphere is comparable to that of the fluid molecules. The diffusivity of a spherical tracer particle is in accord with the Stokes-Einstein relation, and the corresponding Brownian motion is determined by its interaction with the layers formed by fluid molecules around it. When a sphere moves near a solid wall, the drag and torque are found to agree with lubrication theory down to molecular scales, but the predicted divergence is regularized at very short distances due to depletion of fluid molecules near the wall and the appearance of slip at high shear stress. (2) A new mean field theory of sandpiles with dissipation introduced in a clear and physical way has been proposed. All exponents for our model have been obtained by constructing a master equation and mapping the model into a branching process. Two of the exponents are found to depend on a parameter relating the rate of dissipation to that of addition of sand grains to the system whereas the others are universal. A temperature-like parameter T has been introduced in our mean field theory of sandpiles and in growth and evolution models of self-organized criticality. In contrast with evolution and growth models, where the scaling behavior changes dramatically on the introduction of a non-zero temperature, self-organized criticality in sandpiles exists at all T
The many-body localized phase of the quantum random energy model
NASA Astrophysics Data System (ADS)
Baldwin, C. L.; Laumann, C. R.; Pal, A.; Scardicchio, A.
2016-01-01
The random energy model (REM) provides a solvable mean-field description of the equilibrium spin-glass transition. Its quantum sibling (the QREM), obtained by adding a transverse field to the REM, has similar properties and shows a spin-glass phase for sufficiently small transverse field and temperature. In a recent work, some of us have shown that the QREM further exhibits a many-body localization-delocalization (MBLD) transition when viewed as a closed quantum system, evolving according to the quantum dynamics. This phase encloses the familiar equilibrium spin-glass phase. In this paper, we study in detail the MBLD transition within the forward-scattering approximation and replica techniques. The predictions for the transition line are in good agreement with the exact diagonalization numerics. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.
Off-resonant many-body quantum carpets in strongly tilted optical lattices
NASA Astrophysics Data System (ADS)
Muñoz-Arias, Manuel H.; Madroñero, Javier; Parra-Murillo, Carlos A.
2016-04-01
A unit filling Bose-Hubbard Hamiltonian embedded in a strong Stark field is studied in the off-resonant regime inhibiting single- and many-particle first-order tunneling resonances. We investigate the occurrence of coherent dipole wavelike propagation along an optical lattice by means of an effective Hamiltonian accounting for second-order tunneling processes. It is shown that dipole wave function evolution in the short-time limit is ballistic and that finite-size effects induce dynamical self-interference patterns known as quantum carpets. We also present the effects of the border right after the first reflection, showing that the wave function diffuses normally with the variance changing linearly in time. This work extends the rich physical phenomenology of tilted one-dimensional lattice systems in a scenario of many interacting quantum particles, the so-called many-body Wannier-Stark system.
Rotation of quantum impurities in the presence of a many-body environment
NASA Astrophysics Data System (ADS)
Lemeshko, Mikhail; Schmidt, Richard
2015-05-01
Pioneered by the seminal works of Wigner and Racah, the quantum theory of angular momentum evolved into a powerful machinery, commonly used to classify the states of isolated quantum systems and perturbations to their structure due to electromagnetic or crystalline fields. In ``realistic'' experiments, however, quantum systems are almost inevitably coupled to a many-particle environment and a field of elementary excitations associated with it, which is capable of fundamentally altering the physics of the system. We present the first systematic treatment of quantum rotation coupled to a many-particle environment. By using a series of canonical transformations on a generic microscopic Hamiltonian, we single out the conserved quantities of the problem. Using a variational ansatz accounting for an infinite number of many-body excitations, we characterize the spectrum of angular momentum eigenstates and identify the regions of instability, accompanied by emission of angular Cerenkov radiation. The developed technique can be applied to a wide range of systems described by the angular momentum algebra, from Rydberg atoms immersed into BEC's, to cold molecules solvated in helium droplets, to ultracold molecular ions.
The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations
Sellier, J.M. Dimov, I.
2014-09-15
The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.
Exploring Quantum Many-Body Spin Dynamics with Truncated Wigner Methods
NASA Astrophysics Data System (ADS)
Schachenmayer, Johannes
Recent experiments in atomic, molecular, and optical physics offer controlled and clean environments to experimentally study non-equilibrium dynamics of large many-body quantum spin-models with variable range interactions. Thus, efficient computation of such dynamics is of great importance. While in one dimension, time-dependent density matrix renormalization group methods (t-DMRG) have proven effective under certain conditions, computing dynamics in higher dimensional systems remains an outstanding challenge. Recently we formulated the discrete truncated Wigner approximation (DTWA), a semiclassical method based on the truncated Wigner approximation (TWA) that has been proven to be surprisingly accurate in predicting quench dynamics in high-dimensional lattices with up to tens of thousands of quantum spins. Here, we introduce the DTWA and show how it can compute time-evolution of quantum states in experiments that engineer spin-models with polar molecules in optical lattices or with ions in two-dimensional Penning traps. We show, how the DTWA can provide results for the time-evolution of classical and quantum correlations in quench experiments in regimes where other numerical methods are generally unreliable. We report on progress of how to incorporate higher order corrections to the method, and how to adapt it to systems with both spin and bosonic degrees of freedom.
Few-photon transport in many-body photonic systems: A scattering approach
NASA Astrophysics Data System (ADS)
Lee, Changhyoup; Noh, Changsuk; Schetakis, Nikolaos; Angelakis, Dimitris G.
2015-12-01
We study the quantum transport of multiphoton Fock states in one-dimensional Bose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose an optical scheme to probe the underlying many-body states of the system by analyzing the properties of the transmitted light using scattering theory. To this end, we employ the Lippmann-Schwinger formalism within which an analytical form of the scattering matrix can be found. The latter is evaluated explicitly for the two-particle, two-site case which we use to study the resonance properties of two-photon scattering, as well as the scattering probabilities and the second-order intensity correlations of the transmitted light. The results indicate that the underlying structure of the many-body states of the model in question can be directly inferred from the physical properties of the transported photons in its QCA realization. We find that a fully resonant two-photon scattering scenario allows a faithful characterization of the underlying many-body states, unlike in the coherent driving scenario usually employed in quantum master-equation treatments. The effects of losses in the cavities, as well as the incoming photons' pulse shapes and initial correlations, are studied and analyzed. Our method is general and can be applied to probe the structure of any many-body bosonic model amenable to a QCA implementation, including the Jaynes-Cummings-Hubbard model, the extended Bose-Hubbard model, as well as a whole range of spin models.
The nonequilibrium quantum many-body problem as a paradigm for extreme data science
NASA Astrophysics Data System (ADS)
Freericks, J. K.; Nikolić, B. K.; Frieder, O.
2014-12-01
Generating big data pervades much of physics. But some problems, which we call extreme data problems, are too large to be treated within big data science. The nonequilibrium quantum many-body problem on a lattice is just such a problem, where the Hilbert space grows exponentially with system size and rapidly becomes too large to fit on any computer (and can be effectively thought of as an infinite-sized data set). Nevertheless, much progress has been made with computational methods on this problem, which serve as a paradigm for how one can approach and attack extreme data problems. In addition, viewing these physics problems from a computer-science perspective leads to new approaches that can be tried to solve more accurately and for longer times. We review a number of these different ideas here.
Strongdeco: Expansion of analytical, strongly correlated quantum states into a many-body basis
NASA Astrophysics Data System (ADS)
Juliá-Díaz, Bruno; Graß, Tobias
2012-03-01
We provide a Mathematica code for decomposing strongly correlated quantum states described by a first-quantized, analytical wave function into many-body Fock states. Within them, the single-particle occupations refer to the subset of Fock-Darwin functions with no nodes. Such states, commonly appearing in two-dimensional systems subjected to gauge fields, were first discussed in the context of quantum Hall physics and are nowadays very relevant in the field of ultracold quantum gases. As important examples, we explicitly apply our decomposition scheme to the prominent Laughlin and Pfaffian states. This allows for easily calculating the overlap between arbitrary states with these highly correlated test states, and thus provides a useful tool to classify correlated quantum systems. Furthermore, we can directly read off the angular momentum distribution of a state from its decomposition. Finally we make use of our code to calculate the normalization factors for Laughlin's famous quasi-particle/quasi-hole excitations, from which we gain insight into the intriguing fractional behavior of these excitations. Program summaryProgram title: Strongdeco Catalogue identifier: AELA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5475 No. of bytes in distributed program, including test data, etc.: 31 071 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which Mathematica can be installed Operating system: Linux, Windows, Mac Classification: 2.9 Nature of problem: Analysis of strongly correlated quantum states. Solution method: The program makes use of the tools developed in Mathematica to deal with multivariate polynomials to decompose analytical strongly correlated states of bosons and fermions into a standard many-body basis. Operations with polynomials, determinants and permanents are the basic tools. Running time: The distributed notebook takes a couple of minutes to run.
Novel many-body state in quantum wires near pinch-off
NASA Astrophysics Data System (ADS)
Morimoto, T.; Hemmi, M.; Naito, R.; Tsubaki, K.; Aoki, N.; Bird, J. P.; Ochiai, Y.
2007-04-01
We observe novel behavior in the non-linear conductance of semiconductor quantum wires near pinch-off. In this regime, their low-temperature (<1K) differential conductance increases dramatically from zero to a value above 2e2/h. This enhancement depends strongly on temperature, in-plane magnetic field, and wire length. Our results suggest that this resonance is related to the formation of a novel many-body state in the quantum wires near pinch-off.
Many-body two-quantum coherences in 2DFT spectra of semiconductors
NASA Astrophysics Data System (ADS)
Karaiskaj, Denis; Bristow, A.; Dai, X.; Yang, L.; Mukamel, S.; Mirin, R.; Cundiff, S.
2011-03-01
Investigating the correlations of multiple excitons in semiconductors is a challenging many-body problem that has drawn considerable experimental and theoretical attention over the last two decades. Nonlinear four-wave mixing (FWM) experiments have long been known to provide direct probes for the many-body effects in the ultrafast dynamics of excitons in quantum wells. However, it is very difficult to separate the different contributions such as excitation induced dephasing, excitation induced shift, local field effects, and multiple exciton correlations. With the advent of two-dimentional Fourier-transform (2DFT) spectroscopy, the biexcitonic contributions could be isolated and the many-body contributions could be identified. Phase-resolved 2DFT spectra for the negative delay FWM signal will be presented which show interesting diagonal and off-diagonal peaks. The energy positions, line shapes, and the complexity of the 2D peaks indicate significant many-body coherences and reinforce the ability of 2DFT to disentangle two-quantum transitions (D. Karaiskaj, et al., Phys. Rev. Lett. 104, 117401 (2010)).
Dynamics of a Many-Body-Localized System Coupled to a Bath
NASA Astrophysics Data System (ADS)
Fischer, Mark H.; Maksymenko, Mykola; Altman, Ehud
2016-04-01
Coupling a many-body-localized system to a dissipative bath necessarily leads to delocalization. Here, we investigate the nature of the ensuing relaxation dynamics and the information it holds on the many-body-localized state. We formulate the relevant Lindblad equation in terms of the local integrals of motion of the underlying localized Hamiltonian. This allows us to map the quantum evolution deep in the localized state to tractable classical rate equations. We consider two different types of dissipation relevant to systems of ultracold atoms: dephasing due to inelastic scattering on the lattice lasers and particle loss. Our approach allows us to characterize their different effects in the limiting cases of weak and strong interactions.
PREFACE: Advanced many-body and statistical methods in mesoscopic systems
NASA Astrophysics Data System (ADS)
Anghel, Dragos Victor; Sabin Delion, Doru; Sorin Paraoanu, Gheorghe
2012-02-01
It has increasingly been realized in recent times that the borders separating various subfields of physics are largely artificial. This is the case for nanoscale physics, physics of lower-dimensional systems and nuclear physics, where the advanced techniques of many-body theory developed in recent times could provide a unifying framework for these disciplines under the general name of mesoscopic physics. Other fields, such as quantum optics and quantum information, are increasingly using related methods. The 6-day conference 'Advanced many-body and statistical methods in mesoscopic systems' that took place in Constanta, Romania, between 27 June and 2 July 2011 was, we believe, a successful attempt at bridging an impressive list of topical research areas: foundations of quantum physics, equilibrium and non-equilibrium quantum statistics/fractional statistics, quantum transport, phases and phase transitions in mesoscopic systems/superfluidity and superconductivity, quantum electromechanical systems, quantum dissipation, dephasing, noise and decoherence, quantum information, spin systems and their dynamics, fundamental symmetries in mesoscopic systems, phase transitions, exactly solvable methods for mesoscopic systems, various extension of the random phase approximation, open quantum systems, clustering, decay and fission modes and systematic versus random behaviour of nuclear spectra. This event brought together participants from seventeen countries and five continents. Each of the participants brought considerable expertise in his/her field of research and, at the same time, was exposed to the newest results and methods coming from the other, seemingly remote, disciplines. The talks touched on subjects that are at the forefront of topical research areas and we hope that the resulting cross-fertilization of ideas will lead to new, interesting results from which everybody will benefit. We are grateful for the financial and organizational support from IFIN-HH, Ovidius University (where the conference took place), the Academy of Romanian Scientists and the Romanian National Authority for Scientific Research. This conference proceedings volume brings together some of the invited and contributed talks of the conference. The hope of the editors is that they will constitute reference material for applying many-body techniques to problems in mesoscopic and nuclear physics. We thank all the participants for their contribution to the success of this conference. D V Anghel and D S Delion IFIN-HH, Bucharest, Romania G S Paraoanu Aalto University, Finland Conference photograph
Canonical quantization of nonlinear many-body systems.
Scarfone, A M
2005-05-01
We study the quantization of a classical system of interacting particles obeying a recently proposed kinetic interaction principle (KIP) [G. Kaniadakis, Physica A 296, 405 (2001)]. The KIP fixes the expression of the Fokker-Planck equation describing the kinetic evolution of the system and imposes the form of its entropy. In the framework of canonical quantization, we introduce a class of nonlinear Schrödinger equations (NSEs) with complex nonlinearities, describing, in the mean-field approximation, a system of collectively interacting particles whose underlying kinetics is governed by the KIP. We derive the Ehrenfest relations and discuss the main constants of motion arising in this model. By means of a nonlinear gauge transformation of the third kind, it is shown that in the case of constant diffusion and linear drift, the class of NSEs obeying the KIP is gauge-equivalent to another class of NSEs containing purely real nonlinearities depending only on the field rho=|psi|(2) . PMID:16089517
Algorithm for simulation of quantum many-body dynamics using dynamical coarse-graining
Khasin, M.; Kosloff, R.
2010-04-15
An algorithm for simulation of quantum many-body dynamics having su(2) spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables--the elements of the spectrum-generating algebra--is simulated by a surrogate open-system dynamics, which can be interpreted as weak measurement of the target observables, performed on the evolving system. The open-system state can be represented by a mixture of pure states, localized in the phase space. The localization reduces the scaling of the computational resources with the Hilbert-space dimension n by factor n{sup 3/2}(ln n){sup -1} compared to conventional sparse-matrix methods. The guidelines for the choice of parameters for the simulation are presented and the scaling of the computational resources with the Hilbert-space dimension of the system is estimated. The algorithm is applied to the simulation of the dynamics of systems of 2x10{sup 4} and 2x10{sup 6} cold atoms in a double-well trap, described by the two-site Bose-Hubbard model.
Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
Diehl, Sebastian; Micheli, Andrea; Zoller, Peter; Tomadin, Andrea; Fazio, Rosario
2010-07-02
We discuss an open driven-dissipative many-body system, in which the competition of unitary Hamiltonian and dissipative Liouvillian dynamics leads to a nonequilibrium phase transition. It shares features of a quantum phase transition in that it is interaction driven, and of a classical phase transition, in that the ordered phase is continuously connected to a thermal state. We characterize the phase diagram and the critical behavior at the phase transition approached as a function of time. We find a novel fluctuation induced dynamical instability, which occurs at long wavelength as a consequence of a subtle dissipative renormalization effect on the speed of sound.
Cavity quantum electrodynamics with many-body states of a two-dimensional electron gas.
Smolka, Stephan; Wuester, Wolf; Haupt, Florian; Faelt, Stefan; Wegscheider, Werner; Imamoglu, Ataç
2014-10-17
Light-matter interaction has played a central role in understanding as well as engineering new states of matter. Reversible coupling of excitons and photons enabled groundbreaking results in condensation and superfluidity of nonequilibrium quasiparticles with a photonic component. We investigated such cavity-polaritons in the presence of a high-mobility two-dimensional electron gas, exhibiting strongly correlated phases. When the cavity was on resonance with the Fermi level, we observed previously unknown many-body physics associated with a dynamical hole-scattering potential. In finite magnetic fields, polaritons show distinct signatures of integer and fractional quantum Hall ground states. Our results lay the groundwork for probing nonequilibrium dynamics of quantum Hall states and exploiting the electron density dependence of polariton splitting so as to obtain ultrastrong optical nonlinearities. PMID:25278508
Hybrid quantum magnetism in circuit QED: from spin-photon waves to many-body spectroscopy.
Kurcz, Andreas; Bermudez, Alejandro; Garca-Ripoll, Juan Jos
2014-05-01
We introduce a model of quantum magnetism induced by the nonperturbative exchange of microwave photons between distant superconducting qubits. By interconnecting qubits and cavities, we obtain a spin-boson lattice model that exhibits a quantum phase transition where both qubits and cavities spontaneously polarize. We present a many-body ansatz that captures this phenomenon all the way, from a the perturbative dispersive regime where photons can be traced out, to the nonperturbative ultrastrong coupling regime where photons must be treated on the same footing as qubits. Our ansatz also reproduces the low-energy excitations, which are described by hybridized spin-photon quasiparticles, and can be probed spectroscopically from transmission experiments in circuit QED, as shown by simulating a possible experiment by matrix-product-state methods. PMID:24856680
BOOK REVIEW: Many-Body Quantum Theory in Condensed Matter Physics—An Introduction
NASA Astrophysics Data System (ADS)
Logan, D. E.
2005-02-01
This is undoubtedly an ambitious book. It aims to provide a wide ranging, yet self-contained and pedagogical introduction to techniques of quantum many-body theory in condensed matter physics, without losing mathematical `rigor' (which I hope means rigour), and with an eye on physical insight, motivation and application. The authors certainly bring plenty of experience to the task, the book having grown out of their graduate lectures at the Niels Bohr Institute in Copenhagen over a five year period, with the feedback and refinement this presumably brings. The book is also of course ambitious in another sense, for it competes in the tight market of general graduate/advanced undergraduate texts on many-particle physics. Prospective punters will thus want reasons to prefer it to, or at least give it space beside, well established texts in the field. Subject-wise, the book is a good mix of the ancient and modern, the standard and less so. Obligatory chapters deal with the formal cornerstones of many-body theory, from second quantization, time-dependence in quantum mechanics and linear response theory, to Green's function and Feynman diagrams. Traditional topics are well covered, including two chapters on the electron gas, chapters on phonons and electron phonon coupling, and a concise account of superconductivity (confined, no doubt judiciously, to the conventional BCS case). Less mandatory, albeit conceptually vital, subjects are also aired. These include a chapter on Fermi liquid theory, from both semi-classical and microscopic perspectives, and a freestanding account of one-dimensional electron gases and Luttinger liquids which, given the enormity of the topic, is about as concise as it could be without sacrificing clarity. Quite naturally, the authors' own interests also influence the choice of material covered. A persistent theme, which brings a healthy topicality to the book, is the area of transport in mesoscopic systems or nanostructures. Two chapters, some fifty pages of the book, are devoted to electron transport in mesoscopic systems; the one on interacting systems is preceded by a brief account of equation of motion techniques a relative rarity in a general text, used here to provide background to subsequent discussion of the Coulomb blockade in quantum dots. So does it work, and will it find a niche beside other established, wide ranging texts? On the whole I think the answer has to be yes. To begin with, the book is well organised and user-friendly, which must surely appeal to students (and their mentors). The chapters are typically bite-sized and digestible. Each is accompanied by a summary/outlook, which in doing just that attempts to place the specific topic in a wider context, together with a set of problems that illustrate, and in many cases expand substantially on, the basic subject matter. A particularly healthy feature of the book is the extent to which the authors have sought where possible to include physical and/or material applications of basic theory, thereby enlivening old material and enhancing appreciation of the new. The first chapter on the electron gas, for example, introduces the reader to a range of material examples, including 2D heterostructures, carbon nanotubes and quantum dots. A chapter on the formalism of Green's functions takes time out to explain how the single-particle spectral function can be measured by tunnelling spectroscopy, while discussion of impurity scattering and conductivity is refreshed by consideration of weak localization in bulk and mesoscopic systems, and the phenomenon of universal conductance fluctuations. And so on: in a text that could readily descend to the purely formal, the authors have clearly taken seriously the task of incorporating relevant, topical applications of the underlying theory. In a book as wide ranging as this any reviewer is of course bound to perceive the occasional deficiency. I felt for example that some aspects of the discussion of conductance in quantum dots, notably the Coulomb blockade and the Kondo effect, were not quite up to scratch—a touch unbalanced in coverage perhaps (no serious mention of renormalization or scaling, even perturbative), with the odd conceptual error creeping in, and the Kondo effect appearing more mysterious than it really is, possibly in part because consideration of it appears before the chapter on Fermi liquid theory, in which the effect is firmly rooted. But let me not miss the bigger picture: I don't doubt this is a pretty impressive book overall, likely to have broad appeal to budding theorists and adventurous experimentalists, either as a course textbook or—for the slave to garret or lab—as a serious source for self-study. So make a space on your bookshelves.
Collective many-body van der Waals interactions in molecular systems
DiStasio, Robert A.; von Lilienfeld, O. Anatole; Tkatchenko, Alexandre
2012-01-01
Van der Waals (vdW) interactions are ubiquitous in molecules and condensed matter, and play a crucial role in determining the structure, stability, and function for a wide variety of systems. The accurate prediction of these interactions from first principles is a substantial challenge because they are inherently quantum mechanical phenomena that arise from correlations between many electrons within a given molecular system. We introduce an efficient method that accurately describes the nonadditive many-body vdW energy contributions arising from interactions that cannot be modeled by an effective pairwise approach, and demonstrate that such contributions can significantly exceed the energy of thermal fluctuations—a critical accuracy threshold highly coveted during molecular simulations—in the prediction of several relevant properties. Cases studied include the binding affinity of ellipticine, a DNA-intercalating anticancer agent, the relative energetics between the A- and B-conformations of DNA, and the thermodynamic stability among competing paracetamol molecular crystal polymorphs. Our findings suggest that inclusion of the many-body vdW energy is essential for achieving chemical accuracy and therefore must be accounted for in molecular simulations. PMID:22923693
Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap
NASA Astrophysics Data System (ADS)
Haldar, Sudip Kumar; Debnath, Pankaj Kumar; Chakrabarti, Barnali
2013-09-01
We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter ( λ) is slowly tuned from harmonic to anharmonic. For each choice of λ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with larger number of bosons compared to that in the pure harmonic trap. The transition from resonances to bound states with weak anharmonicity also differs significantly from the earlier study of [N. Moiseyev, L.D. Carr, B.A. Malomed, Y.B. Band, J. Phys. B 37, L193 (2004)]. We also study the tunneling of the metastable condensate very close to the critical number N cr of collapse and observe that near collapse the MQT is the dominant decay mechanism compared to the two-body and three-body loss rate. We also observe the power law behavior in MQT near the critical point. The results for pure harmonic trap are in agreement with mean-field results. However, we fail to retrieve the power law behavior in anharmonic trap although MQT is still the dominant decay mechanism.
Many-body effects on intersubband resonances in narrow InAs/AlSb quantum wells
NASA Astrophysics Data System (ADS)
Li, Jianzhong; Ning, C. Z.
2004-01-01
Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (QW) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons. The oscillator strength of intersubband resonances (ISBRs) strongly varies with QW parameters and electron density because of this coupling. Using the intersubband semiconductor Bloch equations for a two-conduction-subband model, we show that intersubband absorption spectra for narrow wells are dominated by the Fermi-edge singularity (via coupling to repellons) when the electron gas becomes degenerate and in the presence of large nonparabolicity. Thus the resonance peak position appears at the Fermi edge and the peak is greatly narrowed, enhanced, and red shifted as compared to the free particle result. Our results uncover a new perspective for ISBRs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBR line shape.
Many-body Effects in a Laterally Inhomogeneous Semiconductor Quantum Well
NASA Technical Reports Server (NTRS)
Ning, Cun-Zheng; Li, Jian-Zhong; Biegel, Bryan A. (Technical Monitor)
2002-01-01
Many body effects on conduction and diffusion of electrons and holes in a semiconductor quantum well are studied using a microscopic theory. The roles played by the screened Hartree-Fock (SHE) terms and the scattering terms are examined. It is found that the electron and hole conductivities depend only on the scattering terms, while the two-component electron-hole diffusion coefficients depend on both the SHE part and the scattering part. We show that, in the limit of the ambipolax diffusion approximation, however, the diffusion coefficients for carrier density and temperature are independent of electron-hole scattering. In particular, we found that the SHE terms lead to a reduction of density-diffusion coefficients and an increase in temperature-diffusion coefficients. Such a reduction or increase is explained in terms of a density-and temperature dependent energy landscape created by the bandgap renormalization.
Radiative heat transfer in anisotropic many-body systems: Tuning and enhancement
Nikbakht, Moladad
2014-09-07
A general formalism for calculating the radiative heat transfer in many body systems with anisotropic component is presented. Our scheme extends the theory of radiative heat transfer in isotropic many body systems to anisotropic cases. In addition, the radiative heating of the particles by the thermal bath is taken into account in our formula. It is shown that the radiative heat exchange (HE) between anisotropic particles and their radiative cooling/heating (RCH) could be enhanced several order of magnitude than that of isotropic particles. Furthermore, we demonstrate that both the HE and RCH can be tuned dramatically by particles relative orientation in many body systems.
Renormalization of myoglobin–ligand binding energetics by quantum many-body effects
Weber, Cédric; Cole, Daniel J.; O’Regan, David D.; Payne, Mike C.
2014-01-01
We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory. This combination of methods explicitly accounts for dynamical and multireference quantum physics, such as valence and spin fluctuations, of the 3d electrons, while treating a significant proportion of the protein (more than 1,000 atoms) with DFT. The computed electronic structure of the myoglobin complexes and the nature of the Fe–O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long-standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of the many-body effects induced by the Hund’s coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin. PMID:24717844
NASA Astrophysics Data System (ADS)
Caballero-Benitez, Santiago F.; Mekhov, Igor B.
2015-12-01
Quantum trapping potentials for ultracold gases change the landscape of classical properties of scattered light and matter. The atoms in a quantum many-body correlated phase of matter change the properties of light and vice versa. The properties of both light and matter can be tuned by design and depend on the interplay between long-range (nonlocal) interactions mediated by an optical cavity and short-range processes of the atoms. Moreover, the quantum properties of light get significantly altered by this interplay, leading the light to have nonclassical features. Further, these nonclassical features can be designed and optimised.
Schreiber, Michael; Hodgman, Sean S; Bordia, Pranjal; Lüschen, Henrik P; Fischer, Mark H; Vosk, Ronen; Altman, Ehud; Schneider, Ulrich; Bloch, Immanuel
2015-08-21
Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions. PMID:26229112
Fokker Planck equations for globally coupled many-body systems with time delays
NASA Astrophysics Data System (ADS)
Frank, T. D.; Beek, P. J.
2005-10-01
A Fokker-Planck description for globally coupled many-body systems with time delays was developed by integrating previously derived Fokker-Planck equations for many-body systems and for time-delayed systems. By means of the Fokker-Planck description developed, we examined the dependence of the variability of many-body systems on attractive coupling forces and time delays. For a fundamental class of systems exemplified by a time-delayed Shimizu-Yamada model for muscular contractions, we established that the variability is an invertible one-to-one mapping of coupling forces and time delays and that coupling forces and time delays have opposite effects on system variability, allowing time delays to annihilate the impact of coupling forces. Furthermore, we showed how variability measures could be used to determine coupling parameters and time delays from experimental data.
More many-body perturbation theory for an electron-ion system
Baker, G.A. Jr.; Johnson, J.D.
1997-10-01
From previous finite-temperature, quantum, many-body perturbation theory results for the grand partition function of an electron-ion fluid through order {epsilon}{sup 4}, we compute the electron and ion fugacities in terms of the volume per ion and the temperature to that same order in perturbation theory. From these results we also give the pressure, again to the same order in perturbation theory about the values for the non-interacting fluid.
Exponential orthogonality catastrophe in single-particle and many-body localized systems
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Pixley, J. H.; Li, Xiaopeng; Das Sarma, S.
2015-12-01
We investigate the statistical orthogonality catastrophe (STOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the STOC gives rise to a wave function overlap between the pre- and postquench ground states that has an exponential decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively "transported" to an arbitrary lattice site. In a many-body localized phase, this nonlocal transport and the associated exponential STOC phenomenon persist in the presence of interactions. We study the possible experimental consequences of the exponential STOC on the Loschmidt echo and spectral function, establishing that this phenomenon might be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy.
Code C# for chaos analysis of relativistic many-body systems
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Felea, D.; Stan, E.; Esanu, T.
2010-08-01
This work presents a new Microsoft Visual C# .NET code library, conceived as a general object oriented solution for chaos analysis of three-dimensional, relativistic many-body systems. In this context, we implemented the Lyapunov exponent and the “fragmentation level” (defined using the graph theory and the Shannon entropy). Inspired by existing studies on billiard nuclear models and clusters of galaxies, we tried to apply the virial theorem for a simplified many-body system composed by nucleons. A possible application of the “virial coefficient” to the stability analysis of chaotic systems is also discussed. Catalogue identifier: AEGH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 30 053 No. of bytes in distributed program, including test data, etc.: 801 258 Distribution format: tar.gz Programming language: Visual C# .NET 2005 Computer: PC Operating system: .Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread RAM: 128 Megabytes Classification: 6.2, 6.5 External routines: .Net Framework 2.0 Library Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, and energy conservation precision test. Additional comments: Easy copy/paste based deployment method. Running time: Quadratic complexity.
Nature of the many-body excitations in a quantum wire: Theory and experiment
NASA Astrophysics Data System (ADS)
Tsyplyatyev, O.; Schofield, A. J.; Jin, Y.; Moreno, M.; Tan, W. K.; Anirban, A. S.; Ford, C. J. B.; Griffiths, J. P.; Farrer, I.; Jones, G. A. C.; Ritchie, D. A.
2016-02-01
The natural excitations of an interacting one-dimensional system at low energy are the hydrodynamic modes of a Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where the quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of R2/L2 , where R is a length-scale related to interactions and L is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analyzed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We have illustrated a crossover to a Luttinger liquid at low energy by calculating the local density of states through all energy scales: from linear to nonlinear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure the momentum-resolved tunneling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe a well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find a structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.
Quantum many-body models with cold atoms coupled to photonic crystals
NASA Astrophysics Data System (ADS)
Douglas, J. S.; Habibian, H.; Hung, C.-L.; Gorshkov, A. V.; Kimble, H. J.; Chang, D. E.
2015-05-01
Using cold atoms to simulate strongly interacting quantum systems is an exciting frontier of physics. However, because atoms are nominally neutral point particles, this limits the types of interaction that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated.
PREFACE: Many-body correlations from dilute to dense nuclear systems
NASA Astrophysics Data System (ADS)
Otsuka, Takaharu; Urban, Michael; Yamada, Taiichi
2011-09-01
The International EFES-IN2P3 conference on "Many body correlations from dilute to dense nuclear systems" was held at the Institut Henri Poincaré (IHP), Paris, France, from 15-18 February 2011, on the occasion of the retirement of our colleague Peter Schuck. Correlations play a decisive role in various many-body systems such as nuclear systems, condensed matter and quantum gases. Important examples include: pairing correlations (Cooper pairs) which give rise to nuclear superfluidity (analogous to superconductivity in condensed matter); particle-hole (RPA) correlations in the description of the ground state beyond mean-field theory; clusters; and α-particle correlations in certain nuclei. Also, the nucleons themselves can be viewed as clusters of three quarks. During the past few years, researchers have started to study how the character of these correlations changes with the variation of the density. For instance, the Cooper pairs in dense matter can transform into a Bose-Einstein condensate (BEC) of true bound states at low density (this is the BCS-BEC crossover studied in ultracold Fermi gases). Similar effects play a role in neutron matter at low density, e.g., in the "neutron skin" of exotic nuclei. The α-cluster correlation becomes particularly important at lower density, such as in the excited states of some nuclei (e.g., the α-condensate-like structure in the Hoyle state of 12C) or in the formation of compact stars. In addition to nuclear physics, topics from astrophysics (neutron stars), condensed matter, and quantum gases were discussed in 48 talks and 19 posters, allowing the almost 90 participants from different communities to exchange their ideas, experiences and methods. The conference dinner took place at the Musée d'Orsay, and all the participants enjoyed the very pleasant atmosphere. One session of the conference was dedicated to the celebration of Peter's retirement. We would like to take this opportunity to wish Peter all the best and we hope that he will continue his scientific work full of creative and original ideas. We would like to thank all those who helped to make the conference a success: Nguyen van Giai, S Fujii, J Margueron, K Hagino, and Y Kanada-En'yo for their help with the organization; the advisory committee for suggesting invited speakers; V Frois for her administrative help; L Petizon for the website; and the director of IPN Orsay, F Azaiez, for his support. We are indebted to IHP for providing the lecture hall free of charge, and we acknowledge the financial support from JSPS through its EFES core-to-core program, from CNRS (IN2P3 and INP), and from LIA France-Japon. Last but not least, we are grateful to all of the participants for making the conference exciting and successful. Takaharu Otsuka, Michael Urban, Taiichi YamadaEditors of the proceedings
Crossover between strong and weak measurement in interacting many-body systems
NASA Astrophysics Data System (ADS)
Esin, Iliya; Romito, Alessandro; Blanter, Ya M.; Gefen, Yuval
2016-01-01
Measurements with variable systemdetector interaction strength, ranging from weak to strong, have been recently reported in a number of electronic nanosystems. In several such instances many-body effects play a significant role. Here we consider the weak-to-strong crossover for a setup consisting of an electronic MachZehnder interferometer, where a second interferometer is employed as a detector. In the context of a conditional which-path protocol, we define a generalized conditional value (GCV), and determine its full crossover between the regimes of weak and strong (projective) measurement. We find that the GCV has an oscillatory dependence on the systemdetector interaction strength. These oscillations are a genuine many-body effect, and can be experimentally observed through the voltage dependence of cross current correlations.
Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Pixley, J. H.; Li, Xiaopeng
We investigate the statistical orthogonality catastrophe (StOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the StOC gives rise to a wave function overlap between the pre- and post-quench ground states that has an exponential decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively ``transported'' to an arbitrary lattice site. We show that in a many-body localized phase, this non-local transport and the associated exponential StOC phenomenon persist in the presence of interactions. We study the possible experimental consequences of the exponential StOC on the Loschmidt echo and spectral function, establishing that this phenomenon might be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy. We thank S.-T. Wang, Z.-X. Gong, Y.-L. Wu, J. D. Sau, and Z. Ovadyahu for discussions. This work is supported by LPS-MPO-CMTC, JQI-NSF-PFC, and ARO-Atomtronics-MURI. The authors acknowledge the University of Maryland supercomputing resources.
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Felea, D.; Esanu, T.; Stan, E.; Bordeianu, C. C.
2013-04-01
In this paper we present a new version of the Chaos Many-Body Engine C# application (Grossu et al. 2012 [1]). In order to benefit from the latest technological advantages, we migrated the application from .Net Framework 2.0 to .Net Framework 4.0. New tools were implemented also. Trying to estimate the particle interactions dependence on initial conditions, we considered a new distance, which takes into account only the structural differences between two systems. We used this distance for implementing the “Structural Lyapunov” function. We propose also a new precision test based on temporal reversed simulations. New version program summaryProgram title: Chaos Many-Body Engine v03 Catalogue identifier: AEGH_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGH_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 214429 No. of bytes in distributed program, including test data, etc.: 9512380 Distribution format: tar.gz Programming language: Visual C# .Net 2010 Computer: PC Operating system: .Net Framework 4.0 running on MS Windows RAM: 128 MB Classification: 24.60.Lz, 05.45.a Catalogue identifier of previous version: AEGH_v2_0 Journal reference of previous version: Computer Physics Communications 183 (2012) 1055-1059 Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm. Implementation of temporal reversed simulation precision test, and “Structural Lyapunov” function. In order to benefit from the advantages involved in the latest technologies (e.g. LINQ Queries [2]), Chaos Many-Body Engine was migrated from .Net Framework 2.0 to .Net Framework 4.0. In addition to existing energy conservation assessment [3], we propose also a reverse simulation precision test. Thus, for a regular simulation, we considered the corresponding reversed process: initial time equals the end time of regular simulation, and temporal resolution dt<0. One can compare the initial state of the regular system, and the final state of the reversed one (t=0) using, for example, the phase-space distance. Trying to measure particle interactions dependence on initial conditions, we considered the following distance, which takes into account only the structure differences between two many-body systems with reactions: ds=√{∑i=1n where Ni1 represents the number of particles of type “i” from the first system, and Ni2 is the corresponding number for the second system. We sum over all particle types. Inspired by the Lyapunov Exponent method [4], we implemented the evolution in time of the “Structural Lyapunov” function, for two identical systems with slightly different initial conditions: Ls(t)=ln ds(t)/ds(0). Migration from .Net Framework 2.0 to .Net Framework 4.0 Reverse simulation precision test “Structural Lyapunov” function. In [1] we applied the Chaos Many-Body Engine to some nuclear relativistic collisions at 4.5 A GeV/c (SKM 200 collaboration [5,6]). We considered also some first tests on He+He head-on collisions at 1 A TeV/c (choose the Simulation∖Collision menu, and set the appropriate parameters Fig. 1). However, in this case, more complex reaction schemas should be considered. Further investigation on higher energies is currently in progress. He+He central, head-on collision at 1 A TeV/c (example of use). Restrictions: The reverse simulation precision test does not apply for: systems with reactions, parallel simulations, and Monte Carlo simulations. Running time: quadratic complexity.
New puzzle for many-body systems with random two-body interactions
Johnson, Calvin W.; Nam, Hai Ah
2007-04-15
We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast J=0,2,4,6,8 states. Previous studies, limited only to J=0,2,4 states, had shown strong correlations in boson systems but not fermion systems. By including J{>=}6 states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.
NASA Astrophysics Data System (ADS)
Wall, Michael
2014-03-01
Experimental progress in generating and manipulating synthetic quantum systems, such as ultracold atoms and molecules in optical lattices, has revolutionized our understanding of quantum many-body phenomena and posed new challenges for modern numerical techniques. Ultracold molecules, in particular, feature long-range dipole-dipole interactions and a complex and selectively accessible internal structure of rotational and hyperfine states, leading to many-body models with long range interactions and many internal degrees of freedom. Additionally, the many-body physics of ultracold molecules is often probed far from equilibrium, and so algorithms which simulate quantum many-body dynamics are essential. Numerical methods which are to have significant impact in the design and understanding of such synthetic quantum materials must be able to adapt to a variety of different interactions, physical degrees of freedom, and out-of-equilibrium dynamical protocols. Matrix product state (MPS)-based methods, such as the density-matrix renormalization group (DMRG), have become the de facto standard for strongly interacting low-dimensional systems. Moreover, the flexibility of MPS-based methods makes them ideally suited both to generic, open source implementation as well as to studies of the quantum many-body dynamics of ultracold molecules. After introducing MPSs and variational algorithms using MPSs generally, I will discuss my own research using MPSs for many-body dynamics of long-range interacting systems. In addition, I will describe two open source implementations of MPS-based algorithms in which I was involved, as well as educational materials designed to help undergraduates and graduates perform research in computational quantum many-body physics using a variety of numerical methods including exact diagonalization and static and dynamic variational MPS methods. Finally, I will mention present research on ultracold molecules in optical lattices, such as the exploration of many-body physics with polyatomic molecules, and the next generation of open source matrix product state codes. This work was performed in the research group of Prof. Lincoln D. Carr.
Quantum many-body theory for qubit decoherence in a finite-size spin bath
Yang Wen; Liu Renbao
2008-11-07
We develop a cluster-correlation expansion theory for the many-body dynamics of a finite-size spin bath in a time scale relevant to the decoherence of a center spin or qubit embedded in the bath. By introducing the cluster correlation as the evolution of a group of bath spins divided by the correlations of all the subgroups, the propagator of the whole bath is factorized into the product of all possible cluster correlations. Each cluster-correlation term accounts for the authentic (non-factorizable) collective excitations within that group. Convergent results can be obtained by truncating the cluster-correlation expansion up to a certain cluster size, as verified in an exactly solvable spin-chain model.
Quantum Optical Lattices for Emergent Many-Body Phases of Ultracold Atoms
NASA Astrophysics Data System (ADS)
Caballero-Benitez, Santiago F.; Mekhov, Igor B.
2015-12-01
Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows us to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some phases appear solely due to quantum light-matter correlations. Because of a global, but spatially structured, interaction, the competition between quantum matter and light waves leads to multimode structures even in single-mode cavities, including delocalized dimers of matter-field coherences (bonds), beyond density orders as supersolids and density waves.
Chaos in fermionic many-body systems and the metal-insulator transition
Papenbrock, T.; Pluhar, Z.; Tithof, J.; Weidenmueller, H. A.
2011-03-15
We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix scaffolding ensemble (ScE) that mimics this transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.
Chaos in Fermionic Many-Body Systems and the Metal Insulator Transition
Papenbrock, Thomas F; Pluhar, Z.; Tithof, J.; Weidenmueller, H. A.
2011-01-01
We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are thus chaotic. Our proof is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble H^{cr} that mimicks that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body is much less sparse than H^{cr}.
Current-carrying quasi-steady states in a periodically driven many-body system
NASA Astrophysics Data System (ADS)
Rudner, Mark; Lindner, Netanel; Berg, Erez
We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially-filled version of Thouless's topologically quantized adiabatic pump. The corresponding single particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For non-integer filling the system is gapless; here the driving cannot be adiabatic and the system is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window where the many-body evolution separately conserves the occupations of the two chiral bands. Within this intermediate time regime we predict that the system reaches a quasi-steady state with uniform crystal momentum occupation within each Floquet band. This state furthermore carries a non-vanishing current given directly by the difference of densities in the right and left moving chiral bands. This remarkable behavior, which holds for both bosons and fermions, may be readily studied experimentally in recently developed cold atom systems.
A driven similarity renormalization group approach to quantum many-body problems
NASA Astrophysics Data System (ADS)
Evangelista, Francesco A.
2014-08-01
Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C2 and F2. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.
A driven similarity renormalization group approach to quantum many-body problems
Evangelista, Francesco A.
2014-08-07
Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C{sub 2} and F{sub 2}. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.
Griffiths effects and slow dynamics in nearly many-body localized systems
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Sarang; Agarwal, Kartiek; Demler, Eugene A.; Huse, David A.; Knap, Michael
2016-04-01
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase." It is known that in one dimension, these rare regions can cause the dc conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wave-vector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.
NASA Astrophysics Data System (ADS)
Mei, Zhongtao; Vidmar, L.; Heidrich-Meisner, F.; Bolech, C. J.
2016-02-01
In the theory of Bethe-ansatz integrable quantum systems, rapidities play an important role as they are used to specify many-body states, apart from phases. The physical interpretation of rapidities going back to Sutherland is that they are the asymptotic momenta after letting a quantum gas expand into a larger volume making it dilute and noninteracting. We exploit this picture to make a direct connection to quantities that are accessible in sudden-expansion experiments with ultracold quantum gases. By a direct comparison of Bethe-ansatz and time-dependent density matrix renormalization group results, we demonstrate that the expansion velocity of a one-dimensional Fermi-Hubbard model can be predicted from knowing the distribution of occupied rapidities defined by the initial state. Curiously, an approximate Bethe-ansatz solution works well also for the Bose-Hubbard model.
Exponential series expansion for correlation functions of many-body systems.
Barocchi, Fabrizio; Guarini, Eleonora; Bafile, Ubaldo
2014-09-01
We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function c(t) can always be expanded in a series of (complex) exponential functions of time when its Laplace transform C̃(z) has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades. Our method is based on a different projection technique in the Hilbert space S of the system and shows that appropriate approximations of the exponential series are related to the contraction of S to a finite, usually small, number of dimensions. The time dependence of correlation functions is always described in detail by a multiple-exponential functionality also at long times. This result is therefore also valid for correlation functions of many-body Hamiltonian systems for which a power-law dependence, observed in restricted time ranges and predicted to be the asymptotic one, can be considered at most as a useful approximate modeling of long-time behavior. PMID:25314394
Exponential series expansion for correlation functions of many-body systems
NASA Astrophysics Data System (ADS)
Barocchi, Fabrizio; Guarini, Eleonora; Bafile, Ubaldo
2014-09-01
We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function c (t) can always be expanded in a series of (complex) exponential functions of time when its Laplace transform C(z) has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades. Our method is based on a different projection technique in the Hilbert space S of the system and shows that appropriate approximations of the exponential series are related to the contraction of S to a finite, usually small, number of dimensions. The time dependence of correlation functions is always described in detail by a multiple-exponential functionality also at long times. This result is therefore also valid for correlation functions of many-body Hamiltonian systems for which a power-law dependence, observed in restricted time ranges and predicted to be the asymptotic one, can be considered at most as a useful approximate modeling of long-time behavior.
Code C# for chaos analysis of relativistic many-body systems with reactions
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Stan, E.; Esanu, T.; Felea, D.; Bordeianu, C. C.
2012-04-01
In this work we present a reaction module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross section, particle lifetime, etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincaré section, we propose also the “Clusterization Map”, as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 Collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular π distributions. Catalogue identifier: AEGH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 184 628 No. of bytes in distributed program, including test data, etc.: 7 905 425 Distribution format: tar.gz Programming language: Visual C#.NET 2005 Computer: PC Operating system: Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread. One processor used for each many-body system. RAM: 128 Megabytes Classification: 6.2, 6.5 Catalogue identifier of previous version: AEGH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1464 External routines: Net Framework 2.0 Library Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems with reactions. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Treatment of two particles reactions and decays. For each particle, calculation of the time measured in the particle reference frame, according to the instantaneous velocity. Possibility to dynamically add particle properties (spin, isospin, etc.), and reactions/decays, using a specific XML input file. Basic support for Monte Carlo simulations. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, “clusterization map”, and energy conservation precision test. As an example of use, we implemented a toy-model for nuclear relativistic collisions at 4.5 A GeV/c. Reasons for new version: Following our goal of applying chaos theory to nuclear relativistic collisions at 4.5 A GeV/c, we developed a reaction module integrated with the Chaos Many-Body Engine. In the previous version, inheriting the Particle class was the only possibility of implementing more particle properties (spin, isospin, and so on). In the new version, particle properties can be dynamically added using a dictionary object. The application was improved in order to calculate the time measured in the own reference frame of each particle. two particles reactions: a+b→c+d, decays: a→c+d, stimulated decays, more complicated schemas, implemented as various combinations of previous reactions. Following our goal of creating a flexible application, the reactions list, including the corresponding properties (cross sections, particles lifetime, etc.), could be supplied as parameter, using a specific XML configuration file. The simulation output files were modified for systems with reactions, assuring also the backward compatibility. We propose the “Clusterization Map” as a new investigation method of many-body systems. The multi-dimensional Lyapunov Exponent was adapted in order to be used for systems with variable structure. Basic support for Monte Carlo simulations was also added. Additional comments: Windows forms application for testing the engine. Easy copy/paste based deployment method. Running time: Quadratic complexity.
Theory of the Many-Body Localization Transition in One-Dimensional Systems
NASA Astrophysics Data System (ADS)
Vosk, Ronen; Huse, David A.; Altman, Ehud
2015-07-01
We formulate a theory of the many-body localization transition based on a novel real-space renormalization group (RG) approach. The results of this theory are corroborated and intuitively explained with a phenomenological effective description of the critical point and of the "badly conducting" state found near the critical point on the delocalized side. The theory leads to the following sharp predictions: (i) The delocalized state established near the transition is a Griffiths phase, which exhibits subdiffusive transport of conserved quantities and sub-ballistic spreading of entanglement. The anomalous diffusion exponent α <1 /2 vanishes continuously at the critical point. The system does thermalize in this Griffiths phase. (ii) The many-body localization transition is controlled by a new kind of infinite-randomness RG fixed point, where the broadly distributed scaling variable is closely related to the eigenstate entanglement entropy. Dynamically, the entanglement grows as ˜log t at the critical point, as it does in the localized phase. (iii) In the vicinity of the critical point, the ratio of the entanglement entropy to the thermal entropy and its variance (and, in fact, all moments) are scaling functions of L /ξ , where L is the length of the system and ξ is the correlation length, which has a power-law divergence at the critical point.
Radiative recombination processes of the many-body states in multiple quantum wells
NASA Astrophysics Data System (ADS)
Cingolani, R.; Ploog, K.; Cingolani, A.; Moro, C.; Ferrara, M.
1990-08-01
The radiative recombination processes of the electron-hole plasma in a series of GaAs/AlxGa1-xAs multiple-quantum-well (MQW) heterostructures have been studied by means of space-resolved high-excitation-intensity luminescence and optical-gain spectroscopy. The spontaneous electron-hole plasma emission dramatically changes depending on the actual MQW heterostructure configuration, which determines the degree of optical confinement in the epilayer. MQW heterostructures consisting of 100 quantum wells or grown on thick barrier layers, exhibit a saturation of the spontaneous emission and high stimulated-emission efficiency. Heterostructures consisting of few quantum wells exhibit the usual high-energy broadening of the luminescence due to the progressive filling of the subbands in the well. Statistical arguments on the photon-mode distribution inside the optical cavity of a semiconductor laser qualitatively account for the observed spectral features. The results of space-resolved luminescence show that the emission spectra of highly excited quantum wells are mostly given by the spectral superposition of the electron-hole plasma emission from the center of the excited region and of excitonic luminescence originating from the lateral region of the excited spot, where the carrier density is lower. These findings are explained by a simple diffusion model taking into account the drift of carriers in the plasma. The optical-gain spectra of suitably designed heterostructures allow us to determine the band-gap renormalization as a function of density of the photogenerated carriers. Additional important information on the ground-level parameters of the electron-hole plasma in GaAs quantum wells is obtained by a line-shape analysis of the optical-gain spectra using an interband recombination model.
Long-range interacting many-body systems with alkaline-earth-metal atoms.
Olmos, B; Yu, D; Singh, Y; Schreck, F; Bongs, K; Lesanovsky, I
2013-04-01
Alkaline-earth-metal atoms can exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the (3)P(0) - (3)D(1) transition of the triplet manifold. In the case of bosonic strontium, which we discuss here, this transition has a wavelength of 2.6 μm and a dipole moment of 4.03 D, and there exists a magic wavelength permitting the creation of optical lattices that are identical for the states (3)P(0) and (3)D(1). This interaction enables the realization and study of mixtures of hard-core lattice bosons featuring long-range hopping, with tunable disorder and anisotropy. We derive the many-body master equation, investigate the dynamics of excitation transport, and analyze spectroscopic signatures stemming from coherent long-range interactions and collective dissipation. Our results show that lattice gases of alkaline-earth-metal atoms permit the creation of long-lived collective atomic states and constitute a simple and versatile platform for the exploration of many-body systems with long-range interactions. As such, they represent an alternative to current related efforts employing Rydberg gases, atoms with large magnetic moment, or polar molecules. PMID:25166986
Equations of state for many-body systems at high densities
NASA Astrophysics Data System (ADS)
Khan, Imran; Gao, Bo
2004-05-01
For a many-body system at high densities, the equation of state depends not only on the scattering length, but also on further details of the inter-particle potential. For a many-atom system, in particular, its behavior at high densities will depend on the van der Waals interaction. We are exploring the behavior of a many-atom system in this density regime using the variational Monte Carlo method, in combination with the concept of effective potential introduced in a recent work(B. Gao, J. Phys. B 36), 2111 (2003).. As an initial test, we will compare our hard-sphere results with those of Gross-Pitevaskii equation and diffussion Monte Carlo method(D. Blume and C. H. Greene, Phys. Rev. A 63), 063601 (2001)..
Dominant role of many-body effects on the carrier distribution function of quantum dot lasers
NASA Astrophysics Data System (ADS)
Peyvast, Negin; Zhou, Kejia; Hogg, Richard A.; Childs, David T. D.
2016-03-01
The effects of free-carrier-induced shift and broadening on the carrier distribution function are studied considering different extreme cases for carrier statistics (Fermi-Dirac and random carrier distributions) as well as quantum dot (QD) ensemble inhomogeneity and state separation using a Monte Carlo model. Using this model, we show that the dominant factor determining the carrier distribution function is the free carrier effects and not the choice of carrier statistics. By using empirical values of the free-carrier-induced shift and broadening, good agreement is obtained with experimental data of QD materials obtained under electrical injection for both extreme cases of carrier statistics.
Entanglement growth in many-body localized systems with long-range interactions
NASA Astrophysics Data System (ADS)
Pino, M.
2014-11-01
We show that von Neumann entropy grows algebraically in time for many-body localized systems with long-range interactions. The dephasing time of far-apart localized degrees of freedom is studied first. For a disentangled high-energy initial state, our analysis indicates that the entropy of one half of the system evolves as t1 /(p +1 ), where p controls the spatial decay of interactions. Numerical simulations of the entropy evolution in the Coulomb and dipolar cases also exhibit an algebraic growth. We find that the saturation value of von Neumann entropy is extensive but small for an ergodic state, and it does not depend on the shape of the interactions. Due to the algebraic entanglement spread, the signature of an extensive entropy should be much easier to observe in experiments with nonlocal interactions than in those with local ones.
Efficient Implementation of Many-body Quantum Chemical Methods on the Intel Xeon Phi Coprocessor
Apra, Edoardo; Klemm, Michael; Kowalski, Karol
2014-12-01
This paper presents the implementation and performance of the highly accurate CCSD(T) quantum chemistry method on the Intel Xeon Phi coprocessor within the context of the NWChem computational chemistry package. The widespread use of highly correlated methods in electronic structure calculations is contingent upon the interplay between advances in theory and the possibility of utilizing the ever-growing computer power of emerging heterogeneous architectures. We discuss the design decisions of our implementation as well as the optimizations applied to the compute kernels and data transfers between host and coprocessor. We show the feasibility of adopting the Intel Many Integrated Core Architecture and the Intel Xeon Phi coprocessor for developing efficient computational chemistry modeling tools. Remarkable scalability is demonstrated by benchmarks. Our solution scales up to a total of 62560 cores with the concurrent utilization of Intel Xeon processors and Intel Xeon Phi coprocessors.
Many-body dispersion corrections for periodic systems: an efficient reciprocal space implementation
NASA Astrophysics Data System (ADS)
Bučko, Tomáš; Lebègue, Sébastien; Gould, Tim; Ángyán, János G.
2016-02-01
The energy and gradient expressions for the many-body dispersion scheme (MBD@rsSCS) of Ambrosetti et al (2014 J. Chem. Phys. 140 18A508) needed for an efficient implementation of the method for systems under periodic boundary conditions are reported. The energy is expressed as a sum of contributions from points sampled in the first Brillouin zone, in close analogy with planewave implementations of the RPA method for electrons in the dielectric matrix formulation. By avoiding the handling of large supercells, considerable computational savings can be achieved for materials with small and medium sized unit cells. The new implementation has been tested and used for geometry optimization and energy calculations of inorganic and molecular crystals, and layered materials.
Heating and many-body resonances in a periodically driven two-band system
NASA Astrophysics Data System (ADS)
Bukov, Marin; Heyl, Markus; Huse, David A.; Polkovnikov, Anatoli
2016-04-01
We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is relatively fast in these two regimes (but to different "temperatures"), in the crossover between them we find slow nonthermalizing time evolution: temporal fluctuations become strong and temporal correlations long lived. Microscopically, we trace back the origin of this nonthermalizing time evolution to the properties of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the approximate energy conservation, and thus produces thermalization to infinite temperature.
Understanding the many-body expansion for large systems. II. Accuracy considerations
NASA Astrophysics Data System (ADS)
Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M.; Herbert, John M.
2016-04-01
To complement our study of the role of finite precision in electronic structure calculations based on a truncated many-body expansion (MBE, or "n-body expansion"), we examine the accuracy of such methods in the present work. Accuracy may be defined either with respect to a supersystem calculation computed at the same level of theory as the n-body calculations, or alternatively with respect to high-quality benchmarks. Both metrics are considered here. In applications to a sequence of water clusters, (H2O)N=6-55 described at the B3LYP/cc-pVDZ level, we obtain mean absolute errors (MAEs) per H2O monomer of ˜1.0 kcal/mol for two-body expansions, where the benchmark is a B3LYP/cc-pVDZ calculation on the entire cluster. Three- and four-body expansions exhibit MAEs of 0.5 and 0.1 kcal/mol/monomer, respectively, without resort to charge embedding. A generalized many-body expansion truncated at two-body terms [GMBE(2)], using 3-4 H2O molecules per fragment, outperforms all of these methods and affords a MAE of ˜0.02 kcal/mol/monomer, also without charge embedding. GMBE(2) requires significantly fewer (although somewhat larger) subsystem calculations as compared to MBE(4), reducing problems associated with floating-point roundoff errors. When compared to high-quality benchmarks, we find that error cancellation often plays a critical role in the success of MBE(n) calculations, even at the four-body level, as basis-set superposition error can compensate for higher-order polarization interactions. A many-body counterpoise correction is introduced for the GMBE, and its two-body truncation [GMBCP(2)] is found to afford good results without error cancellation. Together with a method such as ωB97X-V/aug-cc-pVTZ that can describe both covalent and non-covalent interactions, the GMBE(2)+GMBCP(2) approach provides an accurate, stable, and tractable approach for large systems.
Understanding the many-body expansion for large systems. II. Accuracy considerations.
Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M; Herbert, John M
2016-04-28
To complement our study of the role of finite precision in electronic structure calculations based on a truncated many-body expansion (MBE, or "n-body expansion"), we examine the accuracy of such methods in the present work. Accuracy may be defined either with respect to a supersystem calculation computed at the same level of theory as the n-body calculations, or alternatively with respect to high-quality benchmarks. Both metrics are considered here. In applications to a sequence of water clusters, (H2O)N=6-55 described at the B3LYP/cc-pVDZ level, we obtain mean absolute errors (MAEs) per H2O monomer of ∼1.0 kcal/mol for two-body expansions, where the benchmark is a B3LYP/cc-pVDZ calculation on the entire cluster. Three- and four-body expansions exhibit MAEs of 0.5 and 0.1 kcal/mol/monomer, respectively, without resort to charge embedding. A generalized many-body expansion truncated at two-body terms [GMBE(2)], using 3-4 H2O molecules per fragment, outperforms all of these methods and affords a MAE of ∼0.02 kcal/mol/monomer, also without charge embedding. GMBE(2) requires significantly fewer (although somewhat larger) subsystem calculations as compared to MBE(4), reducing problems associated with floating-point roundoff errors. When compared to high-quality benchmarks, we find that error cancellation often plays a critical role in the success of MBE(n) calculations, even at the four-body level, as basis-set superposition error can compensate for higher-order polarization interactions. A many-body counterpoise correction is introduced for the GMBE, and its two-body truncation [GMBCP(2)] is found to afford good results without error cancellation. Together with a method such as ωB97X-V/aug-cc-pVTZ that can describe both covalent and non-covalent interactions, the GMBE(2)+GMBCP(2) approach provides an accurate, stable, and tractable approach for large systems. PMID:27131529
Many-Body Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge
NASA Astrophysics Data System (ADS)
Li, Xiaopeng; Ganeshan, Sriram; Pixley, J. H.
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge. JQI-NSF-PFC, AROAtomtronics- MURI, and LPS-CMTC, UMD supercomputing resources.
Many-Body Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge
NASA Astrophysics Data System (ADS)
Li, Xiaopeng; Ganeshan, Sriram; Pixley, J. H.; Das Sarma, S.
2015-10-01
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.
Many-Body Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge.
Li, Xiaopeng; Ganeshan, Sriram; Pixley, J H; Das Sarma, S
2015-10-30
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge. PMID:26565483
NASA Astrophysics Data System (ADS)
Tureci, Hakan E.
2013-03-01
Systems of strongly interacting atoms and photons, which can be realized wiring up individual Cavity QED (CQED) systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. Such Lattice CQED systems operate on polaritonic quasi-particles that are hybrids of light and matter in a controllable proportion, combining long-range coherence of photons and strong interactions typically displayed by massive particles. In this talk, I will discuss our recent efforts on the possibility of observing quantum many body physics and quantum phase transitions in Lattice CQED systems. Unavoidable photon loss coupled with the ease of feeding in additional photons through continuous external driving renders such lattices open quantum systems. Another key aspect of many body physics with light that I will focus on is the particle number non-conserving nature of the fundamental light-matter interaction and the question of what quantity, if not the chemical potential, can stabilize finite density quantum phases of correlated photons. Work supported by the NSF and the Swiss NSF. Work reported is a collaboration with M. Biondi, G. Blatter, M. Bordyuh, D. Gerace, A. Houck, J. Keeling, F. Nissen, B. Oztop, M. Schiro, S. Schmidt.
Efficient calculation of many-body induced electrostatics in molecular systems
McLaughlin, Keith Cioce, Christian R.; Pham, Tony; Space, Brian; Belof, Jonathan L.
2013-11-14
Potential energy functions including many-body polarization are in widespread use in simulations of aqueous and biological systems, metal-organics, molecular clusters, and other systems where electronically induced redistribution of charge among local atomic sites is of importance. The polarization interactions, treated here via the methods of Thole and Applequist, while long-ranged, can be computed for moderate-sized periodic systems with extremely high accuracy by extending Ewald summation to the induced fields as demonstrated by Nymand, Sala, and others. These full Ewald polarization calculations, however, are expensive and often limited to very small systems, particularly in Monte Carlo simulations, which may require energy evaluation over several hundred-thousand configurations. For such situations, it shall be shown that sufficiently accurate computation of the polarization energy can be produced in a fraction of the central processing unit (CPU) time by neglecting the long-range extension to the induced fields while applying the long-range treatments of Ewald or Wolf to the static fields; these methods, denoted Ewald E-Static and Wolf E-Static (WES), respectively, provide an effective means to obtain polarization energies for intermediate and large systems including those with several thousand polarizable sites in a fraction of the CPU time. Furthermore, we shall demonstrate a means to optimize the damping for WES calculations via extrapolation from smaller trial systems.
Many-body localization in disorder-free systems: The importance of finite-size constraints
NASA Astrophysics Data System (ADS)
Papić, Z.; Stoudenmire, E. Miles; Abanin, Dmitry A.
2015-11-01
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
NASA Astrophysics Data System (ADS)
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi-patterns exist over a much larger range of physically accessible parameters than the patterns predicted in mean field theory and therefore account for the apparent observations in ecology of patterns in regimes where Turing patterns do not occur. I further show that quasi-patterns have statistical properties that allow them to be distinguished empirically from mean field Turing patterns. I next analyze a model of visual cortex in the brain that has striking similarities to the activator-inhibitor model of ecosystem quasi-pattern formation. Through analysis of the resulting phase diagram, I show that the architecture of the neural network in the visual cortex is configured to make the visual cortex robust to unwanted internally generated spatial structure that interferes with normal visual function. I also predict that some geometric visual hallucinations are quasi-patterns and that the visual cortex supports a new phase of spatially scale invariant behavior present far from criticality. In the final chapter, I explore the effects of fluctuations on cycles in systems biology, specifically the pervasive phenomenon of circadian rhythms. By exploring the behavior of a generic stochastic model of circadian rhythms, I show that the circadian rhythm circuit exploits leaky mRNA production to safeguard the cycle from failure. I also show that this safeguard mechanism is highly robust to changes in the rate of leaky mRNA production. Finally, I explore the failure of the deterministic model in two different contexts, one where the deterministic model predicts cycles where they do not exist, and another context in which cycles are not predicted by the deterministic model.
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions
NASA Astrophysics Data System (ADS)
Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.
Efficient Evaluation of Partition Functions of Inhomogeneous Many-Body Spin Systems
Murg, V.; Cirac, J.I.; Verstraete, F.
2005-07-29
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2D classical spin systems and 1D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite-temperature properties of bosonic particles in 1D optical lattices, as realized in current experiments.
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke
2016-03-01
We introduce the spectrum bifurcation renormalization group (SBRG) as an improved application of the excited-state real-space renormalization group (RSRG-X) for a class of qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to many interacting spin and fermion models in the full MBL phase. As a Hilbert-space preserving RG, SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.
NASA Astrophysics Data System (ADS)
Wang, Yucheng; Hu, Haiping; Chen, Shu
2016-03-01
We study the localization problem of one-dimensional interacting spinless fermions in an incommensurate optical lattice, which changes from an extended phase to a non-ergoic many-body localized phase by increasing the strength of the incommensurate potential. We identify that there exists an intermediate regime before the system enters the many-body localized phase, in which both the localized and extended many-body states coexist, thus the system is divided into three different phases, which can be characterized by normalized participation ratios of the many-body eigenstates and distributions of natural orbitals of the corresponding one-particle density matrix. This is very different from its noninteracting limit, in which all eigenstates undergo a delocalization-localization transition when the strength of the incommensurate potential exceeds a critical value.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-06-01
A simple approach is discussed which associates to (solvable) matrix equations (solvable) dynamical systems, generally interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. We then focus on cases in which the auxiliary variables can be altogether eliminated, reobtaining thereby (via this unified approach) well-known solvable many-body problems, and moreover a (solvable) extension of the "goldfish" model.
NASA Astrophysics Data System (ADS)
Fischer, Uwe R.; Lode, Axel U. Â. J.; Chatterjee, Budhaditya
2015-06-01
The occupation of more than one single-particle state, and hence the emergence of fragmentation, is a many-body phenomenon occurring for systems of spatially confined strongly interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems in single wells. We solve the full many-body Schrödinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method (R-MCTDHB). The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density, and interaction strength is assessed. For contact interactions, it is found that the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long ranged the interactions become. At fixed particle number N , the degree of fragmentation is increasing when the density is decreasing, as expected in one spatial dimension. We demonstrate that this, nontrivially, remains true also for long-range interactions in two spatial dimensions. We, finally, find that fragmentation in a single well is a mesoscopic phenomenon: Within our fully self-consistent approach, the degree of fragmentation, to a good approximation, decreases universally as N-1 /2 when only N is varied.
Understanding the many-body expansion for large systems. I. Precision considerations
NASA Astrophysics Data System (ADS)
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2014-07-01
Electronic structure methods based on low-order "n-body" expansions are an increasingly popular means to defeat the highly nonlinear scaling of ab initio quantum chemistry calculations, taking advantage of the inherently distributable nature of the numerous subsystem calculations. Here, we examine how the finite precision of these subsystem calculations manifests in applications to large systems, in this case, a sequence of water clusters ranging in size up to (H_2O)_{47}. Using two different computer implementations of the n-body expansion, one fully integrated into a quantum chemistry program and the other written as a separate driver routine for the same program, we examine the reproducibility of total binding energies as a function of cluster size. The combinatorial nature of the n-body expansion amplifies subtle differences between the two implementations, especially for n ⩾ 4, leading to total energies that differ by as much as several kcal/mol between two implementations of what is ostensibly the same method. This behavior can be understood based on a propagation-of-errors analysis applied to a closed-form expression for the n-body expansion, which is derived here for the first time. Discrepancies between the two implementations arise primarily from the Coulomb self-energy correction that is required when electrostatic embedding charges are implemented by means of an external driver program. For reliable results in large systems, our analysis suggests that script- or driver-based implementations should read binary output files from an electronic structure program, in full double precision, or better yet be fully integrated in a way that avoids the need to compute the aforementioned self-energy. Moreover, four-body and higher-order expansions may be too sensitive to numerical thresholds to be of practical use in large systems.
Understanding the many-body expansion for large systems. I. Precision considerations
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2014-07-07
Electronic structure methods based on low-order “n-body” expansions are an increasingly popular means to defeat the highly nonlinear scaling of ab initio quantum chemistry calculations, taking advantage of the inherently distributable nature of the numerous subsystem calculations. Here, we examine how the finite precision of these subsystem calculations manifests in applications to large systems, in this case, a sequence of water clusters ranging in size up to (H{sub 2}O){sub 47}. Using two different computer implementations of the n-body expansion, one fully integrated into a quantum chemistry program and the other written as a separate driver routine for the same program, we examine the reproducibility of total binding energies as a function of cluster size. The combinatorial nature of the n-body expansion amplifies subtle differences between the two implementations, especially for n ⩾ 4, leading to total energies that differ by as much as several kcal/mol between two implementations of what is ostensibly the same method. This behavior can be understood based on a propagation-of-errors analysis applied to a closed-form expression for the n-body expansion, which is derived here for the first time. Discrepancies between the two implementations arise primarily from the Coulomb self-energy correction that is required when electrostatic embedding charges are implemented by means of an external driver program. For reliable results in large systems, our analysis suggests that script- or driver-based implementations should read binary output files from an electronic structure program, in full double precision, or better yet be fully integrated in a way that avoids the need to compute the aforementioned self-energy. Moreover, four-body and higher-order expansions may be too sensitive to numerical thresholds to be of practical use in large systems.
Many-body ab-initio diffusion quantum Monte Carlo applied to the strongly correlated oxide NiO
Mitra, Chandrima; Krogel, Jaron T.; Santana, Juan A.; Reboredo, Fernando A.
2015-10-28
We present a many-body diffusion quantum Monte Carlo (DMC) study of the bulk and defect properties of NiO. We find excellent agreement with experimental values, within 0.3%, 0.6%, and 3.5% for the lattice constant, cohesive energy, and bulk modulus, respectively. The quasiparticle bandgap was also computed, and the DMC result of 4.72 (0.17) eV compares well with the experimental value of 4.3 eV. Furthermore, DMC calculations of excited states at the L, Z, and the gamma point of the Brillouin zone reveal a flat upper valence band for NiO, in good agreement with Angle Resolved Photoemission Spectroscopy results. To study defect properties, we evaluated the formation energies of the neutral and charged vacancies of oxygen and nickel in NiO. A formation energy of 7.2 (0.15) eV was found for the oxygen vacancy under oxygen rich conditions. For the Ni vacancy, we obtained a formation energy of 3.2 (0.15) eV under Ni rich conditions. These results confirm that NiO occurs as a p-type material with the dominant intrinsic vacancy defect being Ni vacancy.
Many-body ab-initio diffusion quantum Monte Carlo applied to the strongly correlated oxide NiO
Mitra, Chandrima; Krogel, Jaron T.; Santana, Juan A.; Reboredo, Fernando A.
2015-10-28
We present a many-body diffusion quantum Monte Carlo (DMC) study of the bulk and defect properties of NiO. We find excellent agreement with experimental values, within 0.3%, 0.6%, and 3.5% for the lattice constant, cohesive energy, and bulk modulus, respectively. The quasiparticle bandgap was also computed, and the DMC result of 4.72 (0.17) eV compares well with the experimental value of 4.3 eV. Furthermore, DMC calculations of excited states at the L, Z, and the gamma point of the Brillouin zone reveal a flat upper valence band for NiO, in good agreement with Angle Resolved Photoemission Spectroscopy results. To studymore » defect properties, we evaluated the formation energies of the neutral and charged vacancies of oxygen and nickel in NiO. A formation energy of 7.2 (0.15) eV was found for the oxygen vacancy under oxygen rich conditions. For the Ni vacancy, we obtained a formation energy of 3.2 (0.15) eV under Ni rich conditions. These results confirm that NiO occurs as a p-type material with the dominant intrinsic vacancy defect being Ni vacancy.« less
Bruno, Patrick
2012-06-15
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined. PMID:23004240
Atomic Many-Body Theory Applied to Photoionization Processes in Complex Open-Shell Systems.
NASA Astrophysics Data System (ADS)
Boyle, James John
In this work, we examine the process of photoionization of complex open-shell atoms within the context of many -body perturbation theory (MBPT). A single-particle potential for excited states is introduced which is based on a potential defined by Qian et al.^{[ 1] } Analytic properties of this potential are derived using graphical techniques of angular momentum coupling. Values of the potential are tabulated for all s^{n}, p^{n }, and d^{n} initial state couplings. We have performed a photoionization cross section calculation of atomic tungsten for photon energies from threshold to 150 eV using the generalized resonance technique ^{[ 2]} over several LSJ couplings of the initial state. Although the formalism behind the generalized resonance technique has been discussed previously (ref. 2 of abstract), this work represents the first explicit use of this technique. Non -relativistic orbitals are used in the basis set, and relativistic corrections have been included. We consider excitations from the 4f, 5s, 5p, 5d, and 6s subshells. The effect of the strong 5p^{6}5d^{4} to 5p^{5}5d^5 and 4f^{14}5d^4to 4f ^{13}5d^5 transitions are included as resonant contributions to the 5d partial cross section. Specifically, we consider three LSJ couplings of the 5d subshell in the initial state. For the first case we consider the initial state to be 5d^4[^{5 }D_{J=0}]. In the second we place more emphasis on the J value by diagonalizing the initial state with respect to the spin-orbit Hamiltonian and the eigenstates 5d^4[^ {5}D, _sp{2}{3}P, _sp{4}{3}P, _sp {0}{1}S, _sp{4} {1}S] all coupled to J=0 . Thirdly, we remove the dependence of the initial state upon the J value by computing the cross sections for 5d^4[^{5}D _{j=0,1,2,3,4}], summing the results and weighting by (2J+1). Our results indicate that the 5d partial cross section dominates the total cross section below 100 eV. References. 1. Z. Qian, S. L. Carter, and H. P. Kelly, Phys. Rev. A, 33, 1751 (1986). 2. L. J. Garvin, A Study of Photoionization, including Resonance Structure and Spin-Orbit effects, in Atomic Manganese, Ph.D. Thesis, Univ. of Virginia (unpublished) (1983) pp. 128-45.
Bold-line Monte Carlo and the nonequilibrium physics of strongly correlated many-body systems
NASA Astrophysics Data System (ADS)
Cohen, Guy
2015-03-01
This talk summarizes real time bold-line diagrammatic Monte-Carlo approaches to quantum impurity models, which make significant headway against the sign problem by summing over corrections to self-consistent diagrammatic expansions rather than a bare diagrammatic series. When the bold-line method is combined with reduced dynamics techniques both local single-time properties and two time correlators such as Green functions can be computed at very long timescales, enabling studies of nonequilibrium steady state behavior of quantum impurity models and creating new solvers for nonequilibrium dynamical mean field theory. This work is supported by NSF DMR 1006282, NSF CHE-1213247, DOE ER 46932, TG-DMR120085 and TG-DMR130036, and the Yad Hanadiv-Rothschild Foundation.
Introduction to the Statistical Physics of Integrable Many-body Systems
NASA Astrophysics Data System (ADS)
Šamaj, Ladislav Å.; Bajnok, Zoltán
2013-05-01
Preface; Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index.
Many-body effects on optical gain in GaAsPN/GaPN quantum well lasers for silicon integration
Park, Seoung-Hwan
2014-02-14
Many-body effects on the optical gain in GaAsPN/GaP QW structures were investigated by using the multiband effective-mass theory and the non-Markovian gain model with many-body effects. The free-carrier model shows that the optical gain peak slightly increases with increasing N composition. In addition, the QW structure with a larger As composition shows a larger optical gain than that with a smaller As composition. On the other hand, in the case of the many-body model, the optical gain peak decreases with increasing N composition. Also, the QW structure with a smaller As composition is observed to have a larger optical gain than that with a larger As composition. This can be explained by the fact that the QW structure with a smaller As or N composition shows a larger Coulomb enhancement effect than that with a larger As or N composition. This means that it is important to consider the many-body effect in obtaining guidelines for device design issues.
Multi-meson systems in lattice QCD / Many-body QCD
Detmold, William
2013-08-31
Nuclear physics entails the study of the properties and interactions of hadrons, such as the proton and neutron, and atomic nuclei and it is central to our understanding of our world at the smallest scales. The underlying basis for nuclear physics is provided by the Standard Model of particle physics which describes how matter interacts through the strong, electromagnetic and weak (electroweak) forces. This theory was developed in the 1970s and provides an extremely successful description of our world at the most fundamental level to which it has been probed. The Standard Model has been, and continues to be, subject to stringent tests at particle accelerators around the world, so far passing without blemish. However, at the relatively low energies that are relevant for nuclear physics, calculations involving the strong interaction, governed by the equations of Quantum Chromodynamics (QCD), are enormously challenging, and to date, the only systematic way to perform them is numerically, using a framework known as lattice QCD (LQCD). In this approach, one discretizes space-time and numerically solves the equations of QCD on a space-time lattice; for realistic calculations, this requires highly optimized algorithms and cutting-edge high performance computing (HPC) resources. Progress over the project period is discussed in detail in the following subsections
(The physics of cellular automata and coherence and chaos in classical many-body systems)
Not Available
1992-06-24
This report contains short discussions on the following topics: non-variational effects in a Ginzburg-Landau equation; algebraic correlations in conserved chaotic systems; chaotic interface models of turbulence; algebraic correlations in coupled order parameter systems; and dynamics of Josephson Junction arrays. (LSP)
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-12-01
We take advantage of the simple approach, recently discussed, which associates to (solvable) matrix equations (solvable) dynamical systems interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. Starting from a solvable matrix evolution equation, we obtain the corresponding many-body model and note that in one case the auxiliary variables can be altogether eliminated, obtaining thereby an (also Hamiltonian) extension of the "goldfish" model. The solvability of this novel model, and of its isochronous variant, is exhibited. A related, as well solvable, model, is also introduced, as well as its isochronous variant. Finally, the small oscillations of the isochronous models around their equilibrium configurations are investigated, and from their isochronicity certain diophantine relations are evinced.
Theory of many-body effects in sub-microelectronic systems
NASA Astrophysics Data System (ADS)
Dissado, L. A.; Hill, R. M.
1982-10-01
A new interpretation of the anomalous dispersion process which is observed at low frequencies is presented which is based on a realistic description of the structural ordering and fluctuation in carrier dominated dielectrics. It is shown that this form of response occurs for systems of low spatial dimensionality and generates a sample-size dependent conductivity. The relationship of the mechanism to that of power law noise in electrical systems is identified and the structural interpretation explored. Particular features of hydrogen bonded systems are described in which the dispersion is likely to be important in a biological context. It is pointed out that the process is directly relevant to solid-state batteries such as those based on fast-ion conductors such as Beta-alumina.
Ergodicity in a two-dimensional self-gravitating many-body system
NASA Astrophysics Data System (ADS)
Silvestre, C. H.; Rocha Filho, T. M.
2016-01-01
We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position to the respective ensemble average, sojourn times statistics and the dynamical functional method. For comparison purposes they are also applied to a short-range interacting system and to the Hamiltonian mean-field model. Our results show that a two-dimensional self-gravitating system takes a very long time to establish ergodicity. If a Kac factor is used in the potential energy, such that the total energy is extensive, then this time is independent of particle number, and diverges with √{ N} without a Kac factor.
Course 11: Confinement Technique for Simulating Finite Many-Body Systems
NASA Astrophysics Data System (ADS)
Chekmarev, S. F.
Contents 1 Introduction 2 Key points and advantages of the confinement simulations: General remarks 3 Methods for generating phase trajectories 3.1 Conventional molecular dynamics 3.2 Stochastic molecular dynamics 4 Identification of atomic structures 4.1 Quenching procedure 4.2 Characterization of a minimum 5 Confinement procedures 5.1 Reversal of the trajectory at the boundary of the basin. Microcanonical ensemble 5.2 Initiating the trajectory at the point of the last quenching within the basin. Microcanonical and canonical ensembles 6 Confinement to a selected catchment area. Some applications 6.1 Fractional caloric curves and densities of states of the isomers 6.2 Rates of the transitions between catchment basins. Estimation of the rate of a complex transition by successive confinement 6.3 Creating a subsystem of a complex system. Self-diffusion in the subsystem of permutational isomers 7 Complex study of a system by successive confinement 7.1 Surveying a potential energy surface. Strategies 7.2 Kinetics 7.3 Equilibrium properties 7.4 Study of the alanine tetrapeptide 8 Concluding remarks
Order-disorder transitions in a sheared many-body system
NASA Astrophysics Data System (ADS)
Pfeifer, Jens C.; Bischoff, Tobias; Ehlers, Georg; Eckhardt, Bruno
2015-12-01
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped two-dimensional system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single-particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.
Description of pairing correlation in many-body finite systems with density functional theory
NASA Astrophysics Data System (ADS)
Hupin, Guillaume; Lacroix, Denis
2011-02-01
Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed earlier [D. Lacroix and G. Hupin, Phys. Rev. BPLRBAQ1098-012110.1103/PhysRevB.82.144509 82, 144509 (2010)] are carefully analyzed. Properties of quasiparticle states projected onto good particle numbers are first reviewed. These properties are used to (i) prove the existence of such a functional, (ii) provide an explicit functional through a 1/N expansion starting from the BCS approach, and (iii) give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picket-fence pairing Hamiltonian where even and odd systems are studied, using the blocking technique, at various particle numbers and coupling strengths, with uniform and random single-particle level spacing. In all cases, very good agreement is found, with a deviation of <1% compared to the exact energy.
Image method for Coulomb energy for many-body system of charged dielectric spheres
NASA Astrophysics Data System (ADS)
Qin, Jian; de Pablo, Juan; Freed, Karl
2015-03-01
Ion polarization is important for understanding ion solvation and the stability of ion clusters in polymeric materials which typically exhibit a low and spatially inhomogeneous dielectric permittivity. The simplest approach for modeling ion polarization involves treating the ions as charged spheres with an internal dielectric permittivity differing from that of the medium. The surface polarization contribution to the electrostatic energy for a system of such dielectric spheres can be evaluated perturbatively. We derived closed-form expressions for this energy as a function of the positions of an arbitrary number of polarized surfaces. Our approach is a generalization of the image method for conducting spheres. Using this approach, we calculated the polarization corrections to the cohesion energy for ion clusters and for densely packed ionic crystals. The method can be readily adapted for investigating ion polarization effects in both Monte Carlo and molecular dynamics simulations.
Influence of the interaction range on the thermostatistics of a classical many-body system
NASA Astrophysics Data System (ADS)
Cirto, Leonardo J. L.; Assis, Vladimir R. V.; Tsallis, Constantino
2014-01-01
We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/rα (α≥0). The approach is a first principle one (i.e., based on Newton’s law), and yields the probability distribution of momenta. For α large enough and N≫1 we observe, for longstanding states, the Maxwellian distribution, landmark of Boltzmann-Gibbs thermostatistics. But, for α small or comparable to unity, we observe instead robust fat-tailed distributions that are quite well fitted with q-Gaussians. These distributions extremize, under appropriate simple constraints, the nonadditive entropy Sq upon which nonextensive statistical mechanics is based. The whole scenario appears to be consistent with nonergodicity and with the thesis of the q-generalized Central Limit Theorem.
Multiple-time-scale Landau-Zener transitions in many-body systems
NASA Astrophysics Data System (ADS)
Larson, Jonas
2015-01-01
Motivated by recent cold-atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunneling between neighboring lattice sites this on-site single-particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single-site Landau-Zener transitions, also implies, in the presence of a confining trap, an intersite particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and intersite dynamics. The adiabaticity constraint is therefore not simply given by the standard one, the Hamiltonian rate of change relative to the gap of the on-site problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics; e.g., nonadiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close-to-perfect on-site transitions take place.
Coccia, Emanuele; Varsano, Daniele; Guidoni, Leonardo
2014-02-11
In this letter, we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) Å, larger than the values obtained by DFT (PBE, B3LYP, and CAM-B3LYP) and shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO-LUMO major contribution of the Bu(+)-like (S2) bright excited state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu(+)-like state for the VMC structure (VMC/MBGFT) provide an excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed. PMID:26580027
Relativistic nuclear many-body theory
Serot, B.D. ); Walecka, J.D. . Continuous Electron Beam Accelerator Facility)
1991-09-11
Nonrelativistic models of nuclear systems have provided important insight into nuclear physics. In future experiments, nuclear systems will be examined under extreme conditions of density and temperature, and their response will be probed at momentum and energy transfers larger than the nucleon mass. It is therefore essential to develop reliable models that go beyond the traditional nonrelativistic many-body framework. General properties of physics, such as quantum mechanics, Lorentz covariance, and microscopic causality, motivate the use of quantum field theories to describe the interacting, relativistic, nuclear many-body system. Renormalizable models based on hadronic degrees of freedom (quantum hadrodynamics) are presented, and the assumptions underlying this framework are discussed. Some applications and successes of quantum hadrodynamics are described, with an emphasis on the new features arising from relativity. Examples include the nuclear equation of state, the shell model, nucleon-nucleus scattering, and the inclusion of zero-point vacuum corrections. Current issues and problems are also considered, such as the construction of improved approximations, the full role of the quantum vacuum, and the relationship between quantum hadrodynamics and quantum chromodynamics. We also speculate on future developments. 103 refs., 18 figs.
NASA Astrophysics Data System (ADS)
Grond, Julian; Streltsov, Alexej I.; Lode, Axel U. J.; Sakmann, Kaspar; Cederbaum, Lorenz S.; Alon, Ofir E.
2013-08-01
We derive a general linear-response many-body theory capable of computing excitation spectra of trapped interacting bosonic systems, e.g., depleted and fragmented Bose-Einstein condensates (BECs). To obtain the linear-response equations we linearize the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method, which provides a self-consistent description of many-boson systems in terms of orbitals and a state vector (configurations), and is in principle numerically exact. The derived linear-response many-body theory, which we term LR-MCTDHB, is applicable to systems with interaction potentials of general form. For the special case of a δ interaction potential we show explicitly that the response matrix has a very appealing bilinear form, composed of separate blocks of submatrices originating from contributions of the orbitals, the state vector (configurations), and off-diagonal mixing terms. We further give expressions for the response weights and density response. We introduce the notion of the type of excitations, useful in the study of the physical properties of the equations. From the numerical implementation of the LR-MCTDHB equations and solution of the underlying eigenvalue problem, we obtain excitations beyond available theories of excitation spectra, such as the Bogoliubov-de Gennes (BdG) equations. The derived theory is first applied to study BECs in a one-dimensional harmonic potential. The LR-MCTDHB method contains the BdG excitations and, also, predicts a plethora of additional many-body excitations which are out of the realm of standard linear response. In particular, our theory describes the exact energy of the higher harmonic of the first (dipole) excitation not contained in the BdG theory. We next study a BEC in a very shallow one-dimensional double-well potential. We find with LR-MCTDHB low-lying excitations which are not accounted for by BdG, even though the BEC has only little fragmentation and, hence, the BdG theory is expected to be valid. The convergence of the LR-MCTDHB theory is assessed by systematically comparing the excitation spectra computed at several different levels of theory.
NASA Astrophysics Data System (ADS)
Cingolani, R.; Ploog, K.; Moro, C.; Ferrara, M.
1992-04-01
In the preceding Comment, Hillmer, Hansmann, and Forchel discussed possible mechanisms for the spatial expansion of a photodegenerated electron-hole plasma (EHP) in quantum wells. Although not the major topic of our paper [Phys. Rev. B 42, 2893 (1990)], we agree that excitonic and EHP lateral transport depends strongly on temperature, carrier density, and heterostructure configuration. Our recent results on GaxIn1-xAs/AlyIn1-yAs multiple quantum wells on InP substrate support the idea that wave-guided reabsorption and reemission of the luminescence is responsible for the observed light transport along the crystal surface.
Tkatchenko, Alexandre; Alfè, Dario; Kim, Kwang S
2012-11-13
Supramolecular host-guest systems play an important role for a wide range of applications in chemistry and biology. The prediction of the stability of host-guest complexes represents a great challenge to first-principles calculations due to an interplay of a wide variety of covalent and noncovalent interactions in these systems. In particular, van der Waals (vdW) dispersion interactions frequently play a prominent role in determining the structure, stability, and function of supramolecular systems. On the basis of the widely used benchmark case of the buckyball catcher complex (C60@C60H28), we assess the feasibility of computing the binding energy of supramolecular host-guest complexes from first principles. Large-scale diffusion Monte Carlo (DMC) calculations are carried out to accurately determine the binding energy for the C60@C60H28 complex (26 ± 2 kcal/mol). On the basis of the DMC reference, we assess the accuracy of widely used and efficient density-functional theory (DFT) methods with dispersion interactions. The inclusion of vdW dispersion interactions in DFT leads to a large stabilization of the C60@C60H28 complex. However, DFT methods including pairwise vdW interactions overestimate the stability of this complex by 9-17 kcal/mol compared to the DMC reference and the extrapolated experimental data. A significant part of this overestimation (9 kcal/mol) stems from the lack of dynamical dielectric screening effects in the description of the molecular polarizability in pairwise dispersion energy approaches. The remaining overstabilization arises from the isotropic treatment of atomic polarizability tensors and the lack of many-body dispersion interactions. A further assessment of a different supramolecular system - glycine anhydride interacting with an amide macrocycle - demonstrates that both the dynamical screening and the many-body dispersion energy are complex contributions that are very sensitive to the underlying molecular geometry and type of bonding. We discuss the required improvements in theoretical methods for achieving "chemical accuracy" in the first-principles modeling of supramolecular systems. PMID:26605594
NASA Astrophysics Data System (ADS)
Diehl, S.; Baranov, M.; Daley, A. J.; Zoller, P.
2010-08-01
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).10.1103/PhysRevB.82.064509]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a “continuous supersolid,” which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
Diehl, S.; Daley, A. J.; Zoller, P.; Baranov, M.
2010-08-01
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a 'continuous supersolid', which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martnez, Todd J
2013-09-27
Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions. PMID:24116775
NASA Astrophysics Data System (ADS)
Newman, Timothy
2005-03-01
Inter-cellular communication is essential for coordinated cell movement and spatio-temporal differentiation. Examples are collective behavior of unicellular organisms (such as Dictyostelium aggregation) and formation of structures in multi-cellular organisms (e.g. gastrulation in early embryos). Cells communicate with one another via short-range contact interactions and long-range interactions mediated by chemical signaling fields. In the examples given above the number of cells varies between hundreds to tens of thousands, and the cell population may have strong phenotypic heterogeneity. It is therefore important to develop a model framework which retains discrete cell identity, and allows a flexible description of cell-cell interactions. We present one such framework here, inspired by the many-body formulation of interacting systems, and constructed using approximations which are biologically plausible. We describe a perturbative analysis of chemotactic aggregation, which illustrates the importance of statistical correlations between cells. We also discuss the implementation of this framework as an optimized numerical algorithm, and show some early results on primitive streak formation in the chick embryo.
NASA Astrophysics Data System (ADS)
Freericks, James; Shen, Wen; Devereaux, Tom
2014-03-01
Planck introduced the idea of light quanta to calculate the spectrum for black body radiation, which was employed by Einstein to explain the photoelectric effect. Later, Kubo and Greenwood derived the linear response of a quantum system to an applied external field, and found that the energy available for excitation was determined by the frequency of the driving field as given by the Planck-Einstein relation. As the magnitude of the driving field is further increased into the nonlinear regime, one expects to see multiphoton processes and then for there to be a crossover from frequency-driven excitation of the quantum system to amplitude-driven excitation. Here we use the exact quantum solution of ultracold spinless fermions in a double-well optical lattice driven by an artificial pulsed electric field to show generically how such a crossover occurs. We find that the behavior is quite complex due to excitation and de-excitation processes, so that it is no longer true that tunneling is optimized when the field amplitude is the highest. When the field amplitude becomes very large, there is a novel quantum oscillatory behavior in the excitation spectroscopy that appears to describe a new regime for quantum phenomena. Supported by NSF for algorithm development and DOE for application to the excitation problem.
Case studies in many-body physics
NASA Astrophysics Data System (ADS)
Samolov, Ana
The many-body problem refers to any physical problem made of more than two interacting particles. With increasing number of particles in a system, their coupling and entanglement becomes more complex, and there is no general analytic solution even for a three-body classical or quantum systems. However, some of the most fascinating phenomena in nature are products of collective effects. Therefore, significant efforts have been made in both experiment and theory to unravel some specific many-body problems. If we look at still unanswered physics questions we see that for most of these problems addressing the many-body interactions is a key issue. This field of research is very active, and with the theory relying on multiple approximations specific for the problem at hand, it has become one of the most computationally intensive areas of physics. In this work we address several many-body problems that are still puzzling the scientific community, using different theoretical and computational techniques: 1. Recent experiments in atomic physics considering the proton impact ionization of hydrogen revealed that experimental observations can not be explained with the available theoretical models, developed for more complex helium atom. We used the approximate solution for a three-body Coulomb system to calculate double differential cross sections for proton impact ionization of hydrogen atom, to describe the new experimental findings. 2. One of the central problems in the accelerator science is the interaction of a charged particle beam within itself and matter. Thus, it is crucial that we understand the collective effects governing the scattering of many particles in the bunch on multi center targets. We have developed the particle-particle computational code, based on classical scattering theory, which allows us to include close range interactions between the particles in the study of these many-body effects. 3. In this work we have also considered plasmas, which are manifestation of many-body collective effects. To study the formation of plasmoid-like object in supersonic flow microwave discharge, we have refined the tomographic diagnostic method, so we can take a glance inside this plasma object without disturbing it. The tomographic analysis provided us with spatial distributions of plasma constituents that we need for understanding of the collective-effects in its formation.
Effect of (101¯0) crystal orientation on many-body optical gain of wurtzite InGaN/GaN quantum well
NASA Astrophysics Data System (ADS)
Park, Seoung-Hwan
2003-06-01
The optical properties of (101¯0)-oriented wurtzite (WZ) InGaN/GaN quantum well (QW) lasers are investigated using the multiband effective-mass theory and the non-Markovian gain model with many-body effects. These results are also compared with those of (0001)-oriented WZ InGaN/GaN QW with piezoelectric and spontaneous polarizations taken into account. The optical gain of the (101¯0)-oriented QW is largely enhanced over that of the (0001)-oriented QW. This can be explained by the fact that the optical matrix elements near the band edge (k=0) of the (101¯0)-oriented InGaN/GaN QW significantly increase compared to that of the (0001)-oriented structure, in addition to the reduction of the effective mass. The threshold current density Jth of the (101¯0)-oriented QW is expected to be about half that of the (0001)-oriented QW structure.
Many-body localization for disordered Bosons
NASA Astrophysics Data System (ADS)
Stolz, Günter
2016-03-01
Concrete models of interacting quantum systems for which expected manifestations of the many-body localized phase can be rigorously verified are in short supply. Recent work by Seiringer and Warzel (2016 New J. Phys. 18 035002) succeeds in deriving such properties for a disordered Tonks-Girardeau gas. This provides a first example of a Boson gas in the strong Bose glass phase, characterized by the absence of Bose-Einstein condensation as well as the absence of superfluidity at zero temperature. The derivation exploits new mathematical tools to overcome problems arising from the non-locality of Fermionic wave functions associated with the states of a Tonks-Girardeau gas.
Georgescu, Ionuţ Mandelshtam, Vladimir A.; Jitomirskaya, Svetlana
2013-11-28
Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCP approximation.
NASA Astrophysics Data System (ADS)
Georgescu, IonuÅ£; Jitomirskaya, Svetlana; Mandelshtam, Vladimir A.
2013-11-01
Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCP approximation.
Many-body phenomena in QED-cavity arrays [Invited
Tomadin, A.; Fazio, Rosario
2010-06-15
Coupled quantum electrodynamics (QED) cavities have been recently proposed as new systems to simulate a variety of equilibrium and nonequilibrium many-body phenomena. We present a brief review of their main properties together with a survey of the latest developments of the field and some perspectives concerning their experimental realizations and possible new theoretical directions.
Gravitational Many-Body Problem
Makino, J.
2008-04-29
In this paper, we briefly review some aspects of the gravitational many-body problem, which is one of the oldest problems in the modern mathematical science. Then we review our GRAPE project to design computers specialized to this problem.
NASA Astrophysics Data System (ADS)
Sadd, Michael Alan
This thesis uses computational methods to investigate two very different many body problems. The first half develops a weighted spin-density approximation (WSDA) to the electronic exchange-correlation functional. The second half describes Monte Carlo simulations of the vortex excitation in superfluid helium. After reviewing in Chapter 1 the current status of electronic density functional theory, Chapter 2 develops a fully non-local approximation to the exchange-correlation functional for electrons. The energy functional treats correlation locally and exchange in the WSDA. Atomic ground state energies within this approximation are much improved over those within the popular local spin-density approximation (LSDA). This formulation of the weighted spin-density functional is particularly efficient when applied to problems in quantum chemistry and therefore allows for the first tests of this type of functional on molecules. Results for bond lengths, dissociation energies, and vibrational frequencies for some first row dimers are somewhat disappointing. Chapter 3 argues that this deficit results from an unphysical inter-shell interaction, which underestimates the screening between valence electrons and therefore weakens the bonding. When this interaction is removed in a qualitative fashion, the molecular results show good agreement with experiment. While the resulting form is not elegant, it accurately describes molecular properties. The second part of the thesis describes variational calculations of the properties of a quantum vortex line in both two and three dimensional helium. These Monte Carlo calculations are based on two variations of a "shadow" wave-function. The first generates a singular vortex by simply multiplying the ground state wave-function by a phase. The second form distributes the vorticity over a finite core by exploiting the properties of the "shadow" wave-function. We calculated the radial dependence of the density, velocity field and excitation energy and find that the latter hardly changes as the density is increased from equilibrium to near freezing. This result appears to provide an explanation of why the classical core parameter, obtained from fitting experimental data for the energy and velocity of large vortex rings, expands as the density increases. The last chapter then applies these results to study the binding of a sp3He impurity to a vortex.
NASA Astrophysics Data System (ADS)
Chin, Alex; Prior, Javier; Huelga, Susana F.; Plenio, Martin B.
2011-03-01
Quantum systems which interact strongly with complex and structured environments are receiving increasing attention due to their importance in contexts such as solid-state quantum information processing and bio-molecular quantum dynamics. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively, and standard approaches are invalid or inefficient. Here we combine time-dependent density matrix renormalization group methods with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems at zero and finite temperatures. Using this technique we demonstrate a number of novel dynamical effects which result from long bath memories induced by either sharp spectral structures or strong coupling, and comment on how these can be exploited to drive efficient transport in small networks. We also show how our technique can be used to find the equilibrium properties of excitations in strongly renormalizing environments, and present some results on the quantum phase transition in the sub-Ohmic spin-boson model.
NASA Astrophysics Data System (ADS)
Itin, A. P.; Katsnelson, M. I.
2015-08-01
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role.
Not Available
1992-06-24
This report contains short discussions on the following topics: non-variational effects in a Ginzburg-Landau equation; algebraic correlations in conserved chaotic systems; chaotic interface models of turbulence; algebraic correlations in coupled order parameter systems; and dynamics of Josephson Junction arrays. (LSP)
Ledvinka, Tomás; Schäfer, Gerhard; Bicák, Jirí
2008-06-27
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. PMID:18643648
Many body topics in condensed matter physics
NASA Astrophysics Data System (ADS)
Anduaga, Inaki Pablo
Two different problems involving many-body systems are presented. A hydrodynamic version of the Calogero system of one-dimensional particles interacting on the line is derived using a classical field formalism, and the results are contrasted to a derivation starting from first quantum mechanical principles. This new classical approach is shown to help in understanding subtleties occurring in the latter, such as the conditions for chiral motion, the decomposition of the Hamiltonian in terms of chiral currents and the nature of the physical velocity and density operators. Explicit collective solitonic excitations in the linear and non-linear limits are also presented. Additionally, we overview the possibility of expanding this formalism to the study of the Fractional Quantum Hall Effect. The second problem involves a simple two-dimensional model of a px + ipy superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubovde Gennes operator. The results confirm theoretical predictions such as the Thomas-Fermi approximation and the Ishikawa formula, in which the mass flow at zero-temperature and for a constant director l follows jmass = ½curl(rhohl/2).
Eigenvalues and Low Energy Eigenvectors of Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Muscatello, Christopher Michael
Superthermal ions in tokamak plasmas play a critical role in heating and current drive, and their confinement within the core of the plasma is crucial for obtaining ignition and sustaining burn in future reactors. At the DIII-D tokamak, a suite of fast-ion measurements is available to diagnose various properties of the superthermal population. This thesis work involves a contribution to DIII-D's fast-ion diagnostic collection: the 2nd generation fast-ion deuterium alpha (2G FIDA) detector. FIDA works on the principle of measuring the light that is emitted from neutralized fast ions that undergo charge exchange events with injected neutral atoms. 2G FIDA complements the other FIDA installations on DIII-D with its unique velocity-space sampling volume. Output from a synthetic diagnostic code (FIDAsim) that predicts FIDA emission levels is compared with measurements from 2G FIDA. We find that, while the predicted and measured shapes of the FIDA spectra agree well, the absolute magnitude of the spectral amplitudes are inconsistent. Results from various FIDAsim trials are presented adjusting several parameters, and it is hypothesized that mischaracterization of the diagnostic neutral beams is a major source of error. Instabilities in tokamaks can cause fast-ion transport. The sawtooth instability is particularly important because the crash phase has been observed to cause reductions up to 50% in the central fast-ion density. Passing ions of all energies are redistributed, but only low energy trapped ions suffer redistribution. The observations are consistent with transport by flux-attachment. Comparisons with theory suggest that the intensity of sawtooth-induced transport depends on the magnitude of toroidal drift. Instabilities characterized by toroidal and poloidal mode numbers and real frequency can coherently interact with energetic particles through mode-particle resonances. During a sawtooth crash, even fast ions whose energies are above the threshold for flux-attachment can experience transport if their orbits satisfy the bounce-precessional resonance condition. On DIII-D, a spatially localized population of beam ions accelerated above the injection energy by ion-cyclotron radio frequency (ICRF) heating is diminished at a sawtooth crash. Furthermore, fast-ion losses concurrent with sawtooth crashes are observed. Calculations show that mode-particle resonances could be responsible. Transport of energetic particles by resonant interactions pertains to many types of instabilities; other examples besides sawteeth will also be presented. Analysis shows that large amplitude modes cause significant resonant transport of fast particles. Even small amplitude modes can resonantly drive transport if multiple harmonics exist.
NASA Astrophysics Data System (ADS)
Boyle, J. J.; Pindzola, M. S.
2005-11-01
Preface; Contributors; Introduction; Part I. Atomic Structure: 1. Development of atomic many-body theory Ingvar Lindgren; 2. Relativistic MBPT for highly charged ions W. R. Johnson; 3. Parity nonconservation in atoms S. A. Blundell, W. R. Johnson, and J. Sapirstein; Part II. Photoionization of Atoms: 4. Single photoionization processes J. J. Boyle, and M. D. Kutzner; 5. Photoionization dominated by double excitation T. N. Chang; 6. Direct double photoionization in atoms Z. W. Liu; 7. Photoelectron angular distributions Steven T. Manson; Part III. A. Atomic Scattering - General Considerations: 8. The many-body approach to electron-atom collisions M. Ya Amusia; 9. Theoretical aspects of electron impact ionization P. L. Altick; Part III. B. Atomic Scattering - Low-Order Applications: 10. Perturbation series methods D. H. Madison; 11. Target dependence of the triply differential cross section Cheng Pan and Anthony F. Starace; 12. Overview of Thomas processes for fast mass transfer J. H. McGuire, Jack C. Straton and T. Ishihara; Part III. C. Atomic Scattering - All-Order Applications: 13. R-matrix Theory: Some Recent Applications Philip G. Burke: 14. Electron scattering: application of Dirac R-matrix theory Wasantha Wijesundera, Ian Grant and Patrick Norrington; 15. Close coupling and distorted-wave theory D. C. Griffin and M. S. Pindzola; Appendix: Units and notation; References; Index.
Probing many-body interactions in an optical lattice clock
Rey, A.M.; Gorshkov, A.V.; Kraus, C.V.; Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck ; Martin, M.J.; Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 ; Bishof, M.; Swallows, M.D.; Zhang, X.; Benko, C.; Ye, J.; Lemke, N.D.; Ludlow, A.D.
2014-01-15
We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA {sup 87}Sr and NIST {sup 171}Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems. -- Highlights: •Derived a theoretical framework that describes many-body effects in a lattice clock. •Validated the analysis with recent experimental measurements. •Demonstrated the importance of beyond mean field corrections in the dynamics.
Renormalization group studies of many-body localization
NASA Astrophysics Data System (ADS)
Altman, Ehud
2015-03-01
Quantum correlations do not usually persist for long in systems at finite energy density and disappear once the system thermalizes. But many-body localization offers an alternative paradigm, whereby quantum matter can evade the usual fate of thermal equilibrium and retain retrievable quantum correlations even at high energies. I will survey a dynamical renormalization group (RG) approach used to characterize the novel dynamics and entanglement structures, which develop in the localized phase in lieu of classical thermalization. Then I will present a theory of the transition between the ergodic and the many-body localized phase based on a novel RG framework. Here eigenstate entanglement entropy emerges as a natural scaling variable; the RG describes a change from area-law to volume law entanglement through an intriguing critical point, where the distribution of entanglement entropy becomes maximally broad. The ergodic phase established near the critical point is a Griffiths phase, which exhibits sub-diffusive energy transport and sub-ballistic entanglement propagation. The anomalous diffusion exponent vanishes continuously at the critical point. Before closing I will discuss recent progress in confronting the emerging theoretical understanding of many-body localization with experimental tests. This research is supported in part by the ERC synergy grant UQUAM.
Coccia, Emanuele; Varsano, Daniele; Guidoni, Leonardo
2016-01-01
In this letter, we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) Å, larger than the values obtained by DFT (PBE, B3LYP, and CAM-B3LYP) and shorter than that calculated at the Hartree–Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO–LUMO major contribution of the Bu+-like (S2) bright excited state. Many Body Green’s Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu+-like state for the VMC structure (VMC/MBGFT) provide an excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed. PMID:26580027
Sliusarenko, O. Yu.; Chechkin, A. V.; Slyusarenko, Yu. V.
2015-04-15
By generalizing Bogolyubov’s reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton’s equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the single-particle distribution function, we use a regular cutoff procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation, we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases are discussed by assuming either Gaussian statistics of external perturbation or homogeneity of the system.
Parametric excitation and squeezing in a many-body spinor condensate
Hoang, T. M.; Anquez, M.; Robbins, B. A.; Yang, X. Y.; Land, B. J.; Hamley, C. D.; Chapman, M. S.
2016-01-01
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states. PMID:27044675
Parametric excitation and squeezing in a many-body spinor condensate.
Hoang, T M; Anquez, M; Robbins, B A; Yang, X Y; Land, B J; Hamley, C D; Chapman, M S
2016-01-01
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states. PMID:27044675
Parametric excitation and squeezing in a many-body spinor condensate
NASA Astrophysics Data System (ADS)
Hoang, T. M.; Anquez, M.; Robbins, B. A.; Yang, X. Y.; Land, B. J.; Hamley, C. D.; Chapman, M. S.
2016-04-01
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states.
Many-body localization and thermalization in disordered Hubbard chains
NASA Astrophysics Data System (ADS)
Mondaini, Rubem; Rigol, Marcos
2015-10-01
We study the many-body localization transition in one-dimensional Hubbard chains using exact diagonalization and quantum chaos indicators. We also study dynamics in the delocalized (ergodic) and localized phases and discuss thermalization and eigenstate thermalization, or the lack thereof, in such systems. Consistently within the indicators and observables studied, we find that ergodicity is very robust against disorder, namely, even in the presence of weak Hubbard interactions the disorder strength needed for the system to localize is large. We show that this robustness might be hidden by finite size effects in experiments with ultracold fermions.
Exploring many-body physics with ultracold atoms
NASA Astrophysics Data System (ADS)
LeBlanc, Lindsay Jane
The emergence of many-body physical phenomena from the quantum mechanical properties of atoms can be studied using ultracold alkali gases. The ability to manipulate both Bose-Einstein condensates (BECs) and degenerate Fermi gases (DFGs) with designer potential energy landscapes, variable interaction strengths and out-of-equilibrium initial conditions provides the opportunity to investigate collective behaviour under diverse conditions. With an appropriately chosen wavelength, optical standing waves provide a lattice potential for one target species while ignoring another spectator species. A "tune-in" scheme provides an especially strong potential for the target and works best for Li-Na, Li-K, and K-Na mixtures, while a "tune-out" scheme zeros the potential for the spectator, and is preferred for Li-Cs, K-Rb, Rb-Cs, K-Cs, and 39K-40K mixtures. Species-selective lattices provide unique environments for studying many-body behaviour by allowing for a phonon-like background, providing for effective mass tuning, and presenting opportunities for increasing the phase-space density of one species. Ferromagnetism is manifest in a two-component DFG when the energetically preferred many-body configuration segregates components. Within the local density approximation (LDA), the characteristic energies and the three-body loss rate of the system all give an observable signature of the crossover to this ferromagnetic state in a trapped DFG when interactions are increased beyond kFa(0) = 1:84. Numerical simulations of an extension to the LDA that account for magnetization gradients show that a hedgehog spin texture emerges as the lowest energy configuration in the ferromagnetic regime. Explorations of strong interactions in 40K constitute the first steps towards the realization of ferromagnetism in a trapped 40K gas. The many-body dynamics of a 87Rb BEC in a double well potential are driven by spatial phase gradients and depend on the character of the junction. The amplitude and frequency characteristics of the transport across a tunable barrier show a crossover between two paradigms of super uidity: Josephson plasma oscillations emerge for high barriers, where transport is via tunnelling, while hydrodynamic behaviour dominates for lower barriers. The phase dependence of the many-body dynamics is also evident in the observation of macroscopic quantum self trapping. Gross-Pitaevskii calculations facilitate the interpretation of system dynamics, but do not describe the observed damping.
Studying non-equilibrium many-body dynamics using one-dimensional Bose gases
Langen, Tim; Gring, Michael; Kuhnert, Maximilian; Rauer, Bernhard; Geiger, Remi; Mazets, Igor; Smith, David Adu; Schmiedmayer, Jörg; Kitagawa, Takuya; Demler, Eugene
2014-12-04
Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.
Stochastic gene expression as a many-body problem
Sasai, Masaki; Wolynes, Peter G.
2003-01-01
Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks. PMID:12606710
Many-Body Models for Molecular Nanomagnets
NASA Astrophysics Data System (ADS)
Chiesa, A.; Carretta, S.; Santini, P.; Amoretti, G.; Pavarini, E.
2013-04-01
We present a flexible and effective ab initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as a one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni, and the single-molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.
Many-body coherent destruction of tunneling in photonic lattices
Longhi, Stefano
2011-03-15
An optical realization of the phenomenon of many-body coherent destruction of tunneling, recently predicted for interacting many-boson systems by Gong, Molina, and Haenggi [Phys. Rev. Lett. 103, 133002 (2009)], is proposed for light transport in engineered waveguide arrays. The optical system enables a direct visualization in Fock space of the many-body tunneling control process.
Interferometric probes of many-body localization.
Serbyn, M; Knap, M; Gopalakrishnan, S; Papić, Z; Yao, N Y; Laumann, C R; Abanin, D A; Lukin, M D; Demler, E A
2014-10-01
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems. PMID:25325656
On the Neutrino Self Refraction Problem from a Many-Body Perspective
Pehlivan, Y.; Kajino, Toshitaka; Balantekin, A. B.; Yoshida, Takashi; Maruyama, Tomoyuki
2010-08-12
We consider a dense neutrino gas as a many body system by taking into account both vacuum oscillations and self interactions of neutrinos. We show that the exact many body Hamiltonian which describes the flavor oscillations of such a dense neutrino gas has many constants of motion whose eigenvalues represent a set of good quantum numbers. However, if one adopts the random phase approximation as an effective one particle description, these operators are no longer conserved (i.e. they cease to represent good quantum numbers) although their expectation values are still conserved.
Réal, Florent; Vallet, Valérie; Flament, Jean-Pierre; Masella, Michel
2013-09-21
We present a revised version of the water many-body model TCPE [M. Masella and J.-P. Flament, J. Chem. Phys. 107, 9105 (1997)], which is based on a static three charge sites and a single polarizable site to model the molecular electrostatic properties of water, and on an anisotropic short range many-body energy term specially designed to accurately model hydrogen bonding in water. The parameters of the revised model, denoted TCPE/2013, are here developed to reproduce the ab initio energetic and geometrical properties of small water clusters (up to hexamers) and the repulsive water interactions occurring in cation first hydration shells. The model parameters have also been refined to reproduce two liquid water properties at ambient conditions, the density and the vaporization enthalpy. Thanks to its computational efficiency, the new model range of applicability was validated by performing simulations of liquid water over a wide range of temperatures and pressures, as well as by investigating water liquid/vapor interfaces over a large range of temperatures. It is shown to reproduce several important water properties at an accurate enough level of precision, such as the existence liquid water density maxima up to a pressure of 1000 atm, the water boiling temperature, the properties of the water critical point (temperature, pressure, and density), and the existence of a "singularity" temperature at about 225 K in the supercooled regime. This model appears thus to be particularly well-suited for characterizing ion hydration properties under different temperature and pressure conditions, as well as in different phases and interfaces. PMID:24070292
Many-body effects in semiconductor lasers
Chow, W.W.
1995-03-01
A microscopic theory, that is based on the coupled Maxwell-semiconductor-Bloch equations, is used to investigate the effects of many-body Coulomb interactions in semiconductor laser devices. This paper describes two examples where the many-body effects play important roles. Experimental data supporting the theoretical results are presented.
Relativistically Covariant Many-Body Perturbation Procedure
NASA Astrophysics Data System (ADS)
Lindgren, Ingvar; Salomonson, Sten; Hedendahl, Daniel
A covariant evolution operator (CEO) can be constructed, representing the time evolution of the relativistic wave unction or state vector. Like the nonrelativistic version, it contains (quasi-)singularities. The regular part is referred to as the Green’s operator (GO), which is the operator analogue of the Green’s function (GF). This operator, which is a field-theoretical concept, is closely related to the many-body wave operator and effective Hamiltonian, and it is the basic tool for our unified theory. The GO leads, when the perturbation is carried to all orders, to the Bethe-Salpeter equation (BSE) in the equal-time or effective-potential approximation. When relaxing the equal-time restriction, the procedure is fully compatible with the exact BSE. The calculations are performed in the photonic Fock space, where the number of photons is no longer constant. The procedure has been applied to helium-like ions, and the results agree well with S-matrix results in cases when comparison can be performed. In addition, evaluation of higher-order quantum-electrodynamical (QED) correlational effects has been performed, and the effects are found to be quite significant for light and medium-heavy ions.
Spectral statistics across the many-body localization transition
NASA Astrophysics Data System (ADS)
Serbyn, Maksym; Moore, Joel E.
2016-01-01
The many-body localization transition (MBLT) between ergodic and many-body localized phases in disordered interacting systems is a subject of much recent interest. The statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, a fractal enhancement of matrix elements upon approaching the MBLT from the delocalized side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interactions and the level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories.
Many body population trapping in ultracold dipolar gases
NASA Astrophysics Data System (ADS)
Dutta, Omjyoti; Lewenstein, Maciej; Zakrzewski, Jakub
2014-05-01
A system of interacting dipoles is of paramount importance for understanding many-body physics. The interaction between dipoles is anisotropic and long-range. While the former allows one to observe rich effects due to different geometries of the system, long-range (1/{{r}^{3}}) interactions lead to strong correlations between dipoles and frustration. In effect, interacting dipoles in a lattice form a paradigmatic system with strong correlations and exotic properties with possible applications in quantum information technologies, and as quantum simulators of condensed matter physics, material science, etc. Notably, such a system is extremely difficult to model due to a proliferation of interaction induced multi-band excitations for sufficiently strong dipole-dipole interactions. In this article we develop a consistent theoretical model of interacting polar molecules in a lattice by applying the concepts and ideas of ionization theory which allows us to include highly excited Bloch bands. Additionally, by involving concepts from quantum optics (population trapping), we show that one can induce frustration and engineer exotic states, such as Majumdar-Ghosh state, or vector-chiral states in such a system.
Dynamical stability of a many-body Kapitza pendulum
Citro, Roberta; Dalla Torre, Emanuele G.; D’Alessio, Luca; Polkovnikov, Anatoli; Babadi, Mehrtash; Oka, Takashi; Demler, Eugene
2015-09-15
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.
The semiclassical propagator in Fock space: dynamical echo and many-body interference.
Engl, Thomas; Urbina, Juan Diego; Richter, Klaus
2016-06-13
We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particle contributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal. PMID:27140976
Many-Body Dispersion Interactions in Molecular Materials
NASA Astrophysics Data System (ADS)
Distasio, Robert A., Jr.
2015-03-01
In this work, we have developed an efficient method for obtaining an accurate theoretical description of van der Waals (vdW) interactions that includes both long-range Coulomb electrodynamic response screening effects as well as treatment of the many-body vdW energy to infinite order. This method goes beyond the standard C6 /R6 pairwise additive approximation and can easily be coupled to a wide array of theoretical methods, ranging from classical force fields to higher-level quantum chemical calculations. To demonstrate the increasingly important role played by many-body vdW interactions in large, structurally complex molecular systems, we use this method to investigate several pertinent molecular properties, such as binding energies/affinities in gas-phase molecular dimers and supramolecular complexes, relative conformational energetics in small polypeptides, and thermodynamic stabilities among competing molecular crystal polymorphs. This work received funding from the Department of Energy under Grant Nos.: DOE DE-SC0008626 and DOE DE-FG02ER46201 and the European Research Council (ERC Starting Grant VDW-CMAT).
H theorem for many body collisions
NASA Astrophysics Data System (ADS)
Agbormbai, A. A.
2001-08-01
Although rarefied gas dynamics has traditionally stood on the dilute gas assumption, which supposes that the densities are so low that only binary collisions and single-body gas surface interactions occur, expressions for many-body collision rates and for many-body gas surface interaction (GSI) rates seem to suggest that at lower heights the dilute gas assumption is not valid. In particular, in the pure rarefied regime, two-body GSIs and some three-body interactions occur whereas, in the transition regime into continuum flow, four body collisions and four-body GSIs occur. In this paper I formulate an H theorem for many-body collisions involving atoms. This exercise constitutes the final stage of constructing reciprocity proofs for many body collisions. The first two stages were pursued during the formulation of the many body collision models. They involved demonstrating that reciprocity models for monatomic many-body collisions satisfy detailed balance at equilibrium as well as symmetry with respect to the forward and inverse processes. I begin by deriving the Boltzmann equation for monatomic gases undergoing many body collisions. This leads to the formulation of an elastic collision integral. All these descriptions are carried out in the single-particle phase space of the gas. I formulate the properties of the elastic collision integral and then I use these to formulate an H theorem for reciprocity-based many body collisions. Equilibrium distributions are derived from the approach. An H theorem proof for reciprocity models demonstrates that these models will drive a gas towards equilibrium when used in DSMC computations.
Spatially-partitioned many-body vortices
NASA Astrophysics Data System (ADS)
Klaiman, S.; Alon, O. E.
2016-02-01
A vortex in Bose-Einstein condensates is a localized object which looks much like a tiny tornado storm. It is well described by mean-field theory. In the present work we go beyond the current paradigm and introduce many-body vortices. These are made of spatially- partitioned clouds, carry definite total angular momentum, and are fragmented rather than condensed objects which can only be described beyond mean-field theory. A phase diagram based on a mean-field model assists in predicting the parameters where many-body vortices occur. Implications are briefly discussed.
Local conservation laws and the structure of the many-body localized states.
Serbyn, Maksym; Papić, Z; Abanin, Dmitry A
2013-09-20
We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion. PMID:24093294
Matrix elements of many-body operators and density correlations
Brouder, Christian
2005-09-15
The matrix element of a general many-body operator between two Slater determinants is calculated explicitly. For this, a split-and-pair method is introduced that provides a convenient expression of Wick's theorem and simplifies many-body calculations. The same method is used to determine the generating function of the matrix elements of many-body operators. The split-and-pair method allows also for the diagonalization of the density correlation operators :n(x{sub 1}){center_dot}{center_dot}{center_dot}n(x{sub k}):, where n(x)={psi}{sup {dagger}}(x){psi}(x) is the density operator. The relation between the split-and-pair method and quantum group theory is clarified.
Novel solvable variants of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-02-01
A recent technique to identify solvable many-body problems in two-dimensional space yields, via a new twist, new many-body problems of "goldfish" type. Some of these models are isochronous, namely their generic solutions are completely periodic with a fixed period (independent of the initial data). The investigation of the behavior of some of these isochronous systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations.
How to detect many body localization in experiments
NASA Astrophysics Data System (ADS)
Nandkishore, Rahul
2015-03-01
The standard theory of many body localization (MBL) is framed in terms of exact eigenstates of perfectly isolated quantum systems. However, exact eigenstates can neither be prepared nor measured in the laboratory, and perfectly isolated quantum systems are equally unrealizable. In this talk I explain how MBL can be reformulated without invoking exact eigenstates or perfect isolation. I introduce a way to think about MBL in terms of correlation functions of local operators, evaluated in arbitrary states. This perspective reformulates the standard theory in terms of (in principle) experimentally measurable quantities. Moreover, this ``spectral'' perspective on MBL is far more robust than the conventional ``eigenstate'' perspective. Eigenstates thermalize upon arbitrarily weak coupling to an external environment, but the correlation functions (which are the physical observables) continue to show signatures of MBL as long as the coupling to the environment is weaker than the characteristic energy scales in the system Hamiltonian. I also show how this ``spectral perspective'' can be used to reveal additional structure in the MBL phase, and to make progress on otherwise intractable theory problems. Collaborators: Sarang Gopalakrishnan, David Huse, Sonika Johri, Ravin Bhatt.
Towards Efficient and General Method for Many-Body van-der-Waals Interactions
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2012-02-01
Van der Waals interactions are intrinsically many-body phenomena, arising from collective electron fluctuations in a given material. Adiabatic connection fluctuation-dissipation theorem (ACFDT) allows to compute the many-body vdW interactions accurately. However, the ACFDT computational cost is prohibitive for real materials, even when the random-phase approximation is employed for the response function. We show how the problem of computing the long-range many-body vdW energy for real systems can be solved efficiently by mapping the system (molecule or condensed matter) onto a collection of quantum harmonic oscillators. Currently, our method, which couples density-functional theory with the many-body dispersion energy (DFT+MBD), is developed for non-metallic system [A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, submitted]. The DFT+MBD method includes the hybridization effects by using the Tkatchenko-Scheffler approach [PRL 102, 073005 (2009)], the long-range Coulomb screening through classical electrodynamics [B. U. Felderhof, Physica 29, 1569 (1974)], and the many-body vdW energy from the coupled-fluctuating dipole model [M. W. Cole et al., Mol. Simul. 35, 849 (2009)]. The successes of the DFT+MBD approach and the many challenges that lie ahead will be discussed.
NASA Astrophysics Data System (ADS)
Duguet, T.
2016-05-01
The present contribution summarizes the content and slightly updates the discussion of a recently proposed theoretical analysis of the halo phenomenon in many-fermion systems. We focus here on applications to potential neutron halos in mid-mass nuclei.
Dynamics close to the many-body localization transition
NASA Astrophysics Data System (ADS)
Bar Lev (Krivolapov), Yevgeny; Reichman, David R.
2014-03-01
It has recently been suggested that in a generic class of disordered and (short-ranged) interacting quantum systems a dynamical metal-insulator transition may occur at finite temperatures. This proposed phenomenon is called many-body localization (MBL). In this work we study the real-time dynamics of this transition for a range of parameters where the transition should manifest according to theory and recent numerical studies. For this purpose, we numerically solve the non-equilibrium quantum kinetic equations in the self-consistent second-Born approximation, the same approximation used in the original prediction of MBL. For accessible times, we observe a complex sequence of dynamical regimes. Surprisingly we find little change of behavior upon crossing the putative dynamical phase boundary as determined by previous numerical studies. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. The work was supported by grant NSF-CHE-1213247.
Projection techniques to approach the nuclear many-body problem
NASA Astrophysics Data System (ADS)
Sun, Yang
2016-04-01
Our understanding of angular-momentum-projection goes beyond quantum-number restoration for symmetry-violated states. The angular-momentum-projection method can be viewed as an efficient way of truncating the shell-model space which is otherwise too large to handle. It defines a transformation from the intrinsic system, where dominant excitation modes in the low-energy region are identified with the concept of spontaneous symmetry breaking, to the laboratory frame with well-organized configuration states according to excitations. An energy-dictated, physically-guided shell-model truncation can then be carried out within the projected space and the Hamiltonian is thereby diagonalized in a compact basis. The present article reviews the theory of angular-momentum-projection applied in the nuclear many-body problem. Angular momentum projection emerges naturally if a deformed state is treated quantum-mechanically. To demonstrate how different physical problems in heavy, deformed nuclei can be efficiently described with different truncation schemes, we introduce the projected shell model and show examples of calculation in a basis with axial symmetry, a basis with triaxiality, and a basis with both quasiparticle and phonon excitations. Technical details of how to calculate the projected matrix elements and how to build a workable model with the projection techniques are given in the appendix.
Reboredo, Fernando A
2012-01-01
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\\bf 79}, 195117 (2009), Reboredo, {\\it ibid.} {\\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. A recursive optimization algorithm is derived from the time evolution of the mixed probability density. The mixed probability density is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weigh allows the amplitude of the fix-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC and the fixed-phase approximation [Ortiz, Ceperley and Martin Phys Rev. Lett. {\\bf 71}, 2777 (1993)]. When used recursively it improves simultaneously the node and phase. The algorithm is demonstrated to converge to the nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The method is also applied to obtain low energy excitations with magnetic field or periodic boundary conditions. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.
Absence of many-body mobility edges
NASA Astrophysics Data System (ADS)
De Roeck, Wojciech; Huveneers, Francois; Müller, Markus; Schiulaz, Mauro
2016-01-01
Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur is lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.
PREFACE: 17th International Conference on Recent Progress in Many-Body Theories (MBT17)
NASA Astrophysics Data System (ADS)
Reinholz, Heidi; Boronat, Jordi
2014-08-01
These are the proceedings of the XVII International Conference on Recent Progress in Many-Body Theories, which was held from 8-13 September 2013 in Rostock, Germany. The conference continued the triennial series initiated in Trieste in 1978 and was devoted to new developments in the field of many-body theories. The conference series encourages the exchange of ideas between physicists working in such diverse areas as nuclear physics, quantum chemistry, lattice Hamiltonians or quantum uids. Many-body theories are an integral part in different fields of theoretical physics such as condensed matter, nuclear matter and field theory. Phase transitions and macroscopic quantum effects such as magnetism, Bose-Einstein condensation, super uidity or superconductivity have been investigated within ultra-cold gases, finite systems or various nanomaterials. The conference series on Recent Progress in Many-Body Theories is devoted to foster the interaction and to cross-fertilize between different fields and to discuss future lines of research. The topics of the 17th meeting were Cluster Physics Cold Gases High Energy Density Matter and Intense Lasers Magnetism New Developments in Many-Body Techniques Nuclear Many-Body and Relativistic Theories Quantum Fluids and Solids Quantum Phase Transitions Topological Insulators and Low Dimensional Systems. 109 participants from 20 countries participated. 44 talks and 61 posters werde presented. As a particular highlight of the conference, The Eugene Feenberg Memorial Medal for outstanding results in the field of many-body theory and The Hermann Kümmel Early Achievement Award in Many-Body Physics for young scientists in that field were awarded. The Feenberg Medal went jointly to Patrick Lee (MIT, USA) for his fundamental contributions to condensed-matter theory, especially in regard to the quantum Hall effect, to universal conductance uctuations, and to the Kondo effect in quantum dots, and Douglas Scalapino (UC Santa Barbara, USA) for his imaginative use and development of the Monte-Carlo approach and for his ground-breaking contributions to superconductivity. The Kümmel Award went to Max Metlitski (UC Santa Barbara) for remarkable advances in the theory of quantum criticality in metals. The nominations for the Kümmel Award were of such high standard that the Committee announced Honourable Mentions to Martin Eckstein (MPDS/U Hamburg, Germany) for his leading contributions in the development of non-equilibrium dynamical mean field theory, Emanuel Gull (U Michigan, USA) for the development of the Continuous-Time Auxiliary-Field Quantum Monte Carlo Method and for its use in understanding the interplay of the pseudogap and superconductivity in the Hubbard model and Kai Sun (U Michigan, USA) for seminal contributions to the theory of topological effects in strongly correlated electron systems. The Conference continues the series of conferences held before in Trieste, Italy (1979); Oaxtapec, Mexico (1981); Odenthal-Altenberg, Germany (1983); San Francisco, USA (1985); Oulu, Finland (1987); Arad, Israel (1989); Minneapolis, USA (1991); Schloé Segau, Austria (1994); Sydney, Australia (1997); Seattle, USA (1999); Manchester, UK (2001); Santa Fe, USA (2004); Buenos Aires, Argentina (2005); Barcelona, Spain (2007); Columbus, USA (2009) and Bariloche, Argentina (2011). It has been a great pleasure to prepare for the conference. We thank the IAC and in particular Susana Hernandez and David Neilson as well as the International Programme Committee for their great support and advice. Many more people have been involved locally in organizing this international meeting and thanks goes to them, in particular to the members of the LOC Sonja Lorenzen, Dieter Bauer, Niels-Uwe Bastian, Marina Hertzfeldt, Volker Mosert and Gerd Röpke. The next meeting will take place in Buffalo, USA in 2015 and we look forward to yet another exciting exchange on Recent Progress in Many-Body Theories. Heidi Reinholz and Jordi Boronat Guest editors Conference photograph Details of the committees are available in the PDF.
Many-Body Basis Set Superposition Effect.
Ouyang, John F; Bettens, Ryan P A
2015-11-10
The basis set superposition effect (BSSE) arises in electronic structure calculations of molecular clusters when questions relating to interactions between monomers within the larger cluster are asked. The binding energy, or total energy, of the cluster may be broken down into many smaller subcluster calculations and the energies of these subsystems linearly combined to, hopefully, produce the desired quantity of interest. Unfortunately, BSSE can plague these smaller fragment calculations. In this work, we carefully examine the major sources of error associated with reproducing the binding energy and total energy of a molecular cluster. In order to do so, we decompose these energies in terms of a many-body expansion (MBE), where a "body" here refers to the monomers that make up the cluster. In our analysis, we found it necessary to introduce something we designate here as a many-ghost many-body expansion (MGMBE). The work presented here produces some surprising results, but perhaps the most significant of all is that BSSE effects up to the order of truncation in a MBE of the total energy cancel exactly. In the case of the binding energy, the only BSSE correction terms remaining arise from the removal of the one-body monomer total energies. Nevertheless, our earlier work indicated that BSSE effects continued to remain in the total energy of the cluster up to very high truncation order in the MBE. We show in this work that the vast majority of these high-order many-body effects arise from BSSE associated with the one-body monomer total energies. Also, we found that, remarkably, the complete basis set limit values for the three-body and four-body interactions differed very little from that at the MP2/aug-cc-pVDZ level for the respective subclusters embedded within a larger cluster. PMID:26574311
Many-body characterization of particle-conserving topological superfluids.
Ortiz, Gerardo; Dukelsky, Jorge; Cobanera, Emilio; Esebbag, Carlos; Beenakker, Carlo
2014-12-31
What distinguishes trivial superfluids from topological superfluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our model allows us to identify fermion parity switches that distinctively characterize topological superconductivity (fermion superfluidity) in generic interacting many-body systems. Although the Majorana zero modes in this model have only a power-law confinement, we may still define many-body Majorana operators by tuning the flux to a fermion parity switch. We derive a closed-form expression for an interacting topological invariant and show that the transition away from the topological phase is of third order. PMID:25615376
Goldfishing: A new solvable many-body problem
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-10-01
A recent technique allows one to identify and investigate solvable dynamical systems naturally interpretable as classical many-body problems, being characterized by equations of motion of Newtonian type (generally in two-dimensional space). In this paper we tersely review results previously obtained in this manner and present novel findings of this kind: mainly solvable variants of the goldfish many-body model, including models that feature isochronous classes of completely periodic solutions. Different formulations of these models are presented. The behavior of one of these isochronous dynamical systems in the neighborhood of its equilibrium configuration is investigated, and in this manner some remarkable Diophantine findings are obtained.
Non-equilibrium many body dynamics
Creutz, M.; Gyulassy, M.
1997-09-22
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop.
Rehr, J.J.
1992-12-31
The importance of many-body effects in the theory of XAFS is reviewed. The dominant effects are inelastic losses: Extrinsic losses refer to inelastic losses in the propagation of the photoelectron and are treated using a complex, energy-dependent self-energy. The real part of the self-energy yields an important energy-dependent shift in the phase of the XAFS oscillations, while the imaginary part contributes to the mean-free-path. Intrinsic losses refer to losses associated with the creation of the core-hole. They give rise to shake-up/shake-off contributions to the absorption spectra. These losses may be calculated in terms of a corehole Green`s function. Interference between these processes leads to dynamical corrections, which are important at low energies.
Rehr, J.J.
1992-01-01
The importance of many-body effects in the theory of XAFS is reviewed. The dominant effects are inelastic losses: Extrinsic losses refer to inelastic losses in the propagation of the photoelectron and are treated using a complex, energy-dependent self-energy. The real part of the self-energy yields an important energy-dependent shift in the phase of the XAFS oscillations, while the imaginary part contributes to the mean-free-path. Intrinsic losses refer to losses associated with the creation of the core-hole. They give rise to shake-up/shake-off contributions to the absorption spectra. These losses may be calculated in terms of a corehole Green's function. Interference between these processes leads to dynamical corrections, which are important at low energies.
Particle-hole symmetry, many-body localization, and topological edge modes
NASA Astrophysics Data System (ADS)
Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.
We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).
Recent Progress in Many-Body Theories: Proceedings of the 12th International Conference
NASA Astrophysics Data System (ADS)
Carlson, Joseph A.; Ortiz, Gerardo
2006-07-01
Preface -- International advisory committee -- Feenberg medal session. Surface and superconductivity / L. P. Gor'kov. Spartak T. Belyaev - recipient of the Feenberg Medal / V. Zelevinsky. Many-body physics and spontaneous symmetry breaking / S. T. Belyaev -- Keynote speaker. The future lies ahead / P. W. Anderson -- Strongly correlated systems and phase transitions. Exact results for many-body problems using few-body methods / J. Cardy. Quantum matters: physics beyond Landau's paradigms / T. Senthil. Microscopic calculations of quantum phase transitions in frustrated magnetic lattices / R. F. Bishop & S. E. Krüger. Recent applications of the DMRG method / K. Hallberg. Functional renormalization group in the 2D Hubbard model / C. Honerkamp. Quantum phase transitions and event horizons: condensed matter analogies / G. Chapline. Spin-charge separation and topological phase transitions in Aharnov-Bohm rings of interacting electrons / B. Normand ... [et al.] -- Quantum fluids and solids. Two-particle-two-hole excitations in [symbol]He / E. Krotscheck, H. M. Böhm & K. Schörkhuber. Monolayer charged quantum films: a quantum simulation study / K. Wierschem & E. Manousakis. Can inconmensuration stabilize a superfluid phase of para-hydrogen? / M. Boninsegni. Analysis of the interatomic potential of the helium systems / S. Ujevic & S. A. Vitiello -- Nuclear physics and QCD. Quantum phase transitions in mesoscopic systems / F. Iachello. Nuclear-structure theory in the search for new fundamental physics / J. Engel. Matter at extreme density and its role in neutron stars and supernova / S. Reddy. New approaches to strong coupling lattice QCD / S. Chandrasekharan. Nuclear interactions from the renormalization group / A. Schwenk. Random interactions and ground state spin of finite Fermi systems / V. Zelevinsky & A. Volya -- Cold atoms and quantum information. Superfluid regimes in degenerate atomic fermi gases / G. V. Shlyapnikov. Bosons in optical lattices / S. L. Rolston. Generalized entanglement and quantum phase transitions / R. Somma ... [et al.]. Ground state of many-body lattice systems via a central limit theorem / C. Presilla & M. Ostilli. Effects of a single quantum spin on Josephson oscillations / M. Hru\\vska ... [et al.] -- Complex systems. Spin textures and random fields in dirty quantum hall ferromagnets / J. T. Chalker. Dissipative quantum disordered models / L. F. Cugliandolo. Possibly exact solution for the multicritical point of finite-dimensional spin glasses / H. Nishimori, K. Takeda & T. Sasamoto. From statistical physics methods to algorithms / D. Battaglia, M. Kolař & R. Zecchina.
Uncovering many-body correlations in nanoscale nuclear spin baths by central spin decoherence
Ma, Wen-Long; Wolfowicz, Gary; Zhao, Nan; Li, Shu-Shen; Morton, John J.L.; Liu, Ren-Bao
2014-01-01
Central spin decoherence caused by nuclear spin baths is often a critical issue in various quantum computing schemes, and it has also been used for sensing single-nuclear spins. Recent theoretical studies suggest that central spin decoherence can act as a probe of many-body physics in spin baths; however, identification and detection of many-body correlations of nuclear spins in nanoscale systems are highly challenging. Here, taking a phosphorus donor electron spin in a 29Si nuclear spin bath as our model system, we discover both theoretically and experimentally that many-body correlations in nanoscale nuclear spin baths produce identifiable signatures in decoherence of the central spin under multiple-pulse dynamical decoupling control. We demonstrate that under control by an odd or even number of pulses, the central spin decoherence is principally caused by second- or fourth-order nuclear spin correlations, respectively. This study marks an important step toward studying many-body physics using spin qubits. PMID:25205440
Many-Body Localization Implies that Eigenvectors are Matrix-Product States.
Friesdorf, M; Werner, A H; Brown, W; Scholz, V B; Eisert, J
2015-05-01
The phenomenon of many-body localization has received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at nonzero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalization following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties--a vanishing group velocity and the absence of transport--with entanglement properties of individual eigenvectors. For systems with a generic spectrum, we prove that strong dynamical localization implies that all of its many-body eigenvectors have clustering correlations. The same is true for parts of the spectrum, thus allowing for the existence of a mobility edge above which transport is possible. In one dimension these results directly imply an entanglement area law; hence, the eigenvectors can be efficiently approximated by matrix-product states. PMID:25978216
NASA Astrophysics Data System (ADS)
Clark, John W.; Lucarelli, Dennis G.; Tarn, Tzyh-Jong
2002-12-01
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavours: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.
Particle-hole symmetry, many-body localization, and topological edge modes
NASA Astrophysics Data System (ADS)
Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.
2016-04-01
We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: Even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the noninteracting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders.
On the simulation of indistinguishable fermions in the many-body Wigner formalism
Sellier, J.M. Dimov, I.
2015-01-01
The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.
Diabatic-ramping spectroscopy of many-body excited states
NASA Astrophysics Data System (ADS)
Yoshimura, Bryce; Campbell, W. C.; Freericks, J. K.
2014-12-01
Due to the experimental time constraints of state of the art quantum simulations, the direct preparation of the ground state by adiabatically ramping the field of a transverse-field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping and measures a low-noise observable as a function of time for a constant Hamiltonian to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced, making such experiments feasible with current technology in, for example, ion trap quantum simulators.
Exploring many-body physics with deep networks
NASA Astrophysics Data System (ADS)
Torlai, Giacomo; Carrasquilla, Juan; Schwab, David; Melko, Roger
The introduction of neural networks with deep architecture has led to a revolution, giving rise to a new wave of technologies empowering our modern society. Although data science has been the main focus, the idea of generic algorithms which automatically extract features and representations from raw data is quite general and applicable in multiple scenarios. Motivated by the effectiveness of deep learning algorithms in revealing complex patterns and structures underlying data, we are interested in exploiting such tool in the context of many-body physics. In this talk we will focus on how to extract information about the physics of a many-body system from the generative training of a deep network, and ultimately consider discriminative tasks, such as phase diagrams estimation and critical points detection. We will discuss results for different classical spin systems, including models with quenched disorder.
Influence of dephasing on many-body localization
NASA Astrophysics Data System (ADS)
Medvedyeva, Mariya V.; Prosen, Tomaž; Žnidarič, Marko
2016-03-01
We study the effects of dephasing noise on a prototypical many-body localized system—the X X Z spin 1 /2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process.
Simulating typical entanglement with many-body Hamiltonian dynamics
Nakata, Yoshifumi; Murao, Mio
2011-11-15
We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.
Machine learning for many-body physics: The case of the Anderson impurity model
NASA Astrophysics Data System (ADS)
Arsenault, Louis-François; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Millis, Andrew J.
2014-10-01
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are investigated; a representation in terms of Legendre polynomials is found to be superior due to its limited number of coefficients and its applicability to state of the art methods of solution. The dependence of the errors on the size of the training set is determined. The results indicate that a machine learning approach to dynamical mean-field theory may be feasible.
Charge optimized many-body potential for aluminum.
Choudhary, Kamal; Liang, Tao; Chernatynskiy, Aleksandr; Lu, Zizhe; Goyal, Anuj; Phillpot, Simon R; Sinnott, Susan B
2015-01-14
An interatomic potential for Al is developed within the third generation of the charge optimized many-body (COMB3) formalism. The database used for the parameterization of the potential consists of experimental data and the results of first-principles and quantum chemical calculations. The potential exhibits reasonable agreement with cohesive energy, lattice parameters, elastic constants, bulk and shear modulus, surface energies, stacking fault energies, point defect formation energies, and the phase order of metallic Al from experiments and density functional theory. In addition, the predicted phonon dispersion is in good agreement with the experimental data and first-principles calculations. Importantly for the prediction of the mechanical behavior, the unstable stacking fault energetics along the [Formula: see text] direction on the (1 1 1) plane are similar to those obtained from first-principles calculations. The polycrsytal when strained shows responses that are physical and the overall behavior is consistent with experimental observations. PMID:25407244
Many-body interactions in atomically thin 2D materials
NASA Astrophysics Data System (ADS)
Chernikov, Alexey
2015-03-01
Since the discovery of graphene, a single sheet of carbon atoms, research focused on two-dimensional (2D) materials evolved rapidly due the availability of atomically thin, thermally stable, high-quality crystals with intriguing physical properties. The 2D materials naturally inherit major traits associated with systems of reduced dimensionality: strongly enhanced Coulomb interactions, efficient light-matter coupling, and sensitivity to the environment. In particular, the considerable strength of the Coulomb coupling between the charge carriers introduces a rich variety of many-body phenomena. In the class of 2D semiconductors, e.g., this leads to the emergence of strongly bound electron-hole quasi-particles, such as excitons, trions, and biexcitons, with unusually high binding energies and efficient light absorption. In this talk, I will present a study of the excitonic properties of 2D semiconductors, as exemplified in recent works on atomically thin transition metal dichalcogenides [1-4]. The observation of exciton binding energies on the order of 0.5 eV and the marked deviation of the exciton Rydberg series from the hydrogenic model will be discussed. The results reflect both strong carrier confinement and the distinctive nature of dielectric screening in atomically thin materials. I will further describe how carrier doping and strong photo-excitation can profoundly alter the many-body interactions in these 2D systems.
Nonequilibrium many-body steady states via Keldysh formalism
NASA Astrophysics Data System (ADS)
Maghrebi, Mohammad F.; Gorshkov, Alexey V.
2016-01-01
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
Chiral Symmetry and Many-Body Effect in Multilayer Graphene
NASA Astrophysics Data System (ADS)
Hamamoto, Yuji; Kawarabayashi, Tohru; Aoki, Hideo; Hatsugai, Yasuhiro
2013-08-01
Influence of the chiral symmetry on the many-body problem in multilayer graphene in magnetic fields is investigated. For a spinless electron model on the honeycomb lattice the many-body ground state is shown to be a doubly-degenerate chiral condensate irrespective of the number of layers. The energy spectrum calculated numerically with the exact diagonalization method reveals for ABC-stacked multilayer graphenes that the many-body gap decreases monotonically with the number of layers.
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures. PMID:25144610
Efficient Algorithms for Many-Body Hard Particle Molecular Dynamics
NASA Astrophysics Data System (ADS)
Marín, Mauricio; Risso, Dino; Cordero, Patricio
1993-12-01
Many-body simulations are very CPU-time consuming, making the problem of having efficient algorithms specially relevant. In this paper we propose a strategy--for the simulation of hard particle systems--that is efficient, memory saving, and easy to understand and to program. The time intervals by which the simulation proceeds are the increments between collisions (events), and these are dictated by the system itself. Hence these are event-driven simulations. Our strategy is devised to (a) minimize the number of coordinate updates per event, (b) predict new events only between nearby particles, and (c) efficiently manage the events predicted during the simulation. Empirical results are given to show the performance of our strategy in different computers as well as to compare with other approaches. It is seen that our proposed algorithm is efficient for a wide density range. We also include an analysis of the performance of the strategy proposed.
Many-body formalism for fermions: Testing the enforcement of the Pauli principle
NASA Astrophysics Data System (ADS)
Watson, D. K.
2016-02-01
Enforcing the Pauli principle in many-body systems of fermions to ensure an antisymmetric wave function is typically a numerically expensive task. Numerical methods, such as coupled-cluster, correlated basis function, Monte Carlo, and traditional configuration interaction, scale with powers of N that make the determination of the energy spectrum of these systems a challenge. In a recent paper, we successfully obtained energies for large systems of fermions in the unitary regime in which we applied the Pauli principle "on paper" without obtaining an explicit wave function. This approach, an extension of the symmetry invariant perturbation method to fermions, applies the Pauli principle by imposing restrictions on the quantum numbers used to obtain the energy. As a followup to this study, we perform an explicit test of the validity of this application of the Pauli principle by comparing our energy results against the energies corresponding to explicitly antisymmetrized wave functions for an exactly solvable system of harmonically confined, harmonically interacting fermions. Our results show that our simple method of applying the Pauli principle selects from a spectrum of possible many-body energies only those energies that correspond to explicitly antisymmetrized wave functions. Our results were tested for values of N through ≈10 000 and for weak and strong interactions both repulsive and attractive.
Many-body formalism for fermions: Enforcing the Pauli principle on paper
NASA Astrophysics Data System (ADS)
Watson, D. K.
2015-07-01
Confined quantum systems involving N identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with N and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.
Long tail distributions near the many-body localization transition
NASA Astrophysics Data System (ADS)
Luitz, David J.
2016-04-01
The random field S =1/2 Heisenberg chain exhibits a dynamical many body localization transition at a critical disorder strength, which depends on the energy density. At weak disorder, the eigenstate thermalization hypothesis (ETH) is fulfilled on average, making local observables smooth functions of energy, whose eigenstate-to-eigenstate fluctuations decrease exponentially with system size. We demonstrate the validity of ETH in the thermal phase as well as its breakdown in the localized phase and show that rare states exist which do not strictly follow ETH, becoming more frequent closer to the transition. Similarly, the probability distribution of the entanglement entropy at intermediate disorder develops long tails all the way down to zero entanglement. We propose that these low entanglement tails stem from localized regions at the subsystem boundaries which were recently discussed as a possible mechanism for subdiffusive transport in the ergodic phase.
A Many-Body Field Theory Approach to Stochastic Models in Population Biology
Dodd, Peter J.; Ferguson, Neil M.
2009-01-01
Background Many models used in theoretical ecology, or mathematical epidemiology are stochastic, and may also be spatially-explicit. Techniques from quantum field theory have been used before in reaction-diffusion systems, principally to investigate their critical behavior. Here we argue that they make many calculations easier and are a possible starting point for new approximations. Methodology We review the many-body field formalism for Markov processes and illustrate how to apply it to a ‘Brownian bug’ population model, and to an epidemic model. We show how the master equation and the moment hierarchy can both be written in particularly compact forms. The introduction of functional methods allows the systematic computation of the effective action, which gives the dynamics of mean quantities. We obtain the 1-loop approximation to the effective action for general (space-) translation invariant systems, and thus approximations to the non-equilibrium dynamics of the mean fields. Conclusions The master equations for spatial stochastic systems normally take a neater form in the many-body field formalism. One can write down the dynamics for generating functional of physically-relevant moments, equivalent to the whole moment hierarchy. The 1-loop dynamics of the mean fields are the same as those of a particular moment-closure. PMID:19730742
Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
The self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem. Phys. {\\bf 136}, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. {\\bf 89}, 6316 (1988)] are blended to obtain a method for the calculation of thermodynamic properties of many-body systems at low temperatures. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric trial wave functions. A statistical method is derived for the calculation of finite temperature properties of many-body systems near the ground state. In the process we also obtain a parallel algorithm that optimizes the many-body basis of a small subspace of the many-body Hilbert space. This small subspace is optimized to have maximum overlap with the one expanded by the lower energy eigenstates of a many-body Hamiltonian. We show in a model system that the Helmholtz free energy is minimized within this subspace as the iteration number increases. We show that the subspace expanded by the small basis systematically converges towards the subspace expanded by the lowest energy eigenstates. Possible applications of this method to calculate the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.
Extended slow dynamical regime close to the many-body localization transition
NASA Astrophysics Data System (ADS)
Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
2016-02-01
Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L =28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S (t ) ∝t1 /z with a disorder-dependent exponent z ≥1 , in contrast with the pure ballistic growth z =1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t ) ∝t-ζ with a continuously varying disorder-dependent exponent ζ , vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.
Investigation of many-body forces in krypton and xenon
Salacuse, J.J.; Egelstaff, P.A.
1988-10-15
The simplicity of the state dependence at relatively high temperatures ofthe many-body potential contribution to the pressure and energy has been pointed out previously (J. Ram and P. A. Egelstaff, J. Phys. Chem. Liq. 14, 29 (1984); A. Teitsima and P. A. Egelstaff, Phys. Rev. A 21, 367 (1980)). In this paper, we investigate how far these many-body potential terms may be represented by simple models in the case of krypton on the 423-, 273-, 190-, and 150-K isotherms, and xenon on the 170-, 210-, and 270-K isotherms. At the higher temperatures the best agreement is found for the mean-field type of theory, and some consequences are pointed out. On the lower isotherms a state point is found where the many-body energy vanishes, and large departures from mean-field behavior are observed. This is attributed to the influence of short-ranged many-body forces.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
NASA Astrophysics Data System (ADS)
Hermes, Matthew R.; Hirata, So
2014-08-01
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm-1 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic many-body perturbation theory for anharmonic molecular vibrations.
Hermes, Matthew R; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm(-1) and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects. PMID:25173003
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Hermes, Matthew R.; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Communication: Random phase approximation renormalized many-body perturbation theory
NASA Astrophysics Data System (ADS)
Bates, Jefferson E.; Furche, Filipp
2013-11-01
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.
Communication: Random phase approximation renormalized many-body perturbation theory
Bates, Jefferson E.; Furche, Filipp
2013-11-07
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.
Exploring the few- to many-body crossover using cold atoms in one dimension
NASA Astrophysics Data System (ADS)
Zinner, Nikolaj Thomas
2016-03-01
Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a 'cool' quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.
NASA Astrophysics Data System (ADS)
Lode, Axel U. J.; Chakrabarti, Barnali; Kota, Venkata K. B.
2015-09-01
We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of N =10 interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schrödinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a nontrivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that mean-field approaches such as the time-dependent Gross-Pitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (R-MCTDHB).
Understanding many-body physics in one dimension from the Lieb-Liniger model
NASA Astrophysics Data System (ADS)
Jiang, Yu-Zhu; Chen, Yang-Yang; Guan, Xi-Wen
2015-05-01
This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb-Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe’s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb-Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang-Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb-Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability. Project supported by the National Basic Research Program of China (Grant No. 2012CB922101) and the National Natural Science Foundation of China (Grant Nos. 11374331 and 11304357).
Many-body theory of chemotactic cell-cell interactions.
Newman, T J; Grima, R
2004-11-01
We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling epsilon , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient D(R)--an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that D(R) is renormalized to zero at a critical value of epsilon, indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that D(R) approximately epsilon(-2) , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion. PMID:15600665
Many-body theory of chemotactic cell-cell interactions
NASA Astrophysics Data System (ADS)
Newman, T. J.; Grima, R.
2004-11-01
We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling γ , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient DR —an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that DR is renormalized to zero at a critical value of γ , indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that DR˜γ-2 , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion.
On the representation of many-body interactions in water
Medders, Gregory R.; Gotz, Andreas W.; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-09
Our recent work has shown that the many-body expansion of the interactionenergy can be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and long-range interactions at different orders is investigated by analyzing water potentials that treat the leading terms of the many-body expansion through implicit (i.e., TTM3-F and TTM4-F PESs) and explicit (i.e., WHBB and MB-pol PESs) representations. Moreover, it is found that explicit short-range representations of 2-body and 3-body interactions along with a physically correct incorporation of short- and long-range contributions are necessary for an accurate representation of the waterinteractions from the gas to the condensed phase. Likewise, a complete many-body representation of the dipole moment surface is found to be crucial to reproducing the correct intensities of the infrared spectrum of liquid water.
Pichler, H.; Daley, A. J.; Zoller, P.
2010-12-15
We analyze in detail the heating of bosonic atoms in an optical lattice due to incoherent scattering of light from the lasers forming the lattice. Because atoms scattered into higher bands do not thermalize on the time scale of typical experiments, this process cannot be described by the total energy increase in the system alone (which is determined by single-particle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the many-body physics of the state. We characterize the effects on many-body states for various system parameters, where we observe important differences in the heating for strongly and weakly interacting regimes, as well as a strong dependence on the sign of the laser detuning from the excited atomic state. We compute heating rates and changes to characteristic correlation functions based on both perturbation-theory calculations and a time-dependent calculation of the dissipative many-body dynamics. The latter is made possible for one-dimensional systems by combining time-dependent density-matrix-renormalization-group methods with quantum trajectory techniques.
Tsatsos, Marios C.; Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.
2010-09-15
A three-dimensional attractive Bose-Einstein condensate is expected to collapse when the number of the particles N in the ground state or the interaction strength {lambda}{sub 0} exceeds a critical value. We study systems of different particle numbers and interaction strength and find that even if the overall ground state is collapsed there is a plethora of fragmented excited states that are still in the metastable region. Utilizing the configuration interaction expansion we determine the spectrum of the ground (''yrast'') and excited many-body states with definite total angular-momentum quantum numbers 0{<=}L{<=}N and -L{<=}M{sub L{<=}}L, and we find and examine states that survive the collapse. This opens up the possibility of realizing a metastable system with overcritical numbers of bosons in a ground state with angular momentum L{ne}0. The multiorbital mean-field theory predictions about the existence of fragmented metastable states with overcritical numbers of bosons are verified and elucidated at the many-body level. The descriptions of the total angular momentum within the mean-field and the many-body approaches are compared.
Particle diagrams and statistics of many-body random potentials
NASA Astrophysics Data System (ADS)
Small, Rupert A.; Müller, Sebastian
2015-05-01
We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the method of supersymmetry and the eigenvector expansion technique pioneered in Benet et al. (2001). We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with m bosons or fermions that interact through a random k-body Hermitian potential (k ≤ m); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble (eGUE) (Mon and French, 1975). Our results apply in the limit where the number l of available single-particle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semi-circular level density for m < 2 k to Gaussian moments in the dilute limit k ≪ m ≪ l. Regarding the form of this transition, we see that as m is increased, more and more diagrams become relevant, with new contributions starting from each of the points m = 2 k , 3 k , … , nk for the 2 nth moment.
Many-body localization and symmetry protected topology with ultracold Rydberg atoms
NASA Astrophysics Data System (ADS)
Potirniche, Ionut-Dragos; Schleier-Smith, Monika; Vishwanath, Ashvin; Yao, Norman
The interplay between quantum entanglement and symmetry-protected topological order has led to the classification of gapped, interacting, one dimensional quantum phases. A consequence of this classification is the existence of a diverse set of exactly solvable models, which serve as paradigmatic examples of various SPT orders. The experimental realization of such models has been hampered by the challenge of implementing tunable multi-body interactions. Recently, an alternate strategy has arisen: periodic driving. Indeed, it has been shown that the dynamics of a simple Floquet transverse-field Ising model can mirror that of the celebrated Haldane chain. However, as SPT order is expected only in the ground state while a driven system is expected to heat to infinite temperature, the ability to observe such ``Floquet'' SPT phases remains an open question. Here, we demonstrate that strong disorder, leading to many-body localization, stabilizes SPT order at finite energy densities while also preventing arbitrary heating of the system. Moreover, we propose a natural experimental implementation in a 1D optical lattice of ultracold Rydberg atoms.
NASA Astrophysics Data System (ADS)
Hu, Hui; Wang, An-Bang; Yi, Su; Liu, Xia-Ji
2016-05-01
We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasiperiodic (bichromatic) optical lattice within a standard variational approach. We consider both repulsive and attractive contact interactions for such a simple many-body localization problem of Fermi polarons. The variational approach enables us to access relatively large systems and therefore may be used to understand many-body localization in the thermodynamic limit. The energy and wave function of the polaron states are found to be strongly affected by the quasirandom lattice potential and their experimental measurements (i.e., via radio-frequency spectroscopy or quantum gas microscope) therefore provide a sensitive way to underpin the localization transition. We determine a phase diagram by calculating two critical quasirandom disorder strengths, which correspond to the onset of the localization of the ground-state polaron state and the many-body localization of all polaron states, respectively. Our predicted phase diagram could be straightforwardly examined in current cold-atom experiments.
Many-body interactions in quasi-freestanding graphene
Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei; Louie, Steven; Lanzara, Alessandra
2011-06-03
The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.
Many-body interactions in quasi-freestanding graphene.
Siegel, David A; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei V; Louie, Steven G; Lanzara, Alessandra
2011-07-12
The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions. PMID:21709258
Many-body polarization effects and the membrane dipole potential.
Harder, E.; MacKerell, A. D.; Roux, B.
2009-01-01
Molecular dynamics simulations of a lipid monolayer at a water-air interface are used to investigate the dipole potential that arises at the water-lipid interface. One simulation explicitly accounts for many-body polarization effects by using a model based on classical Drude oscillators. The dipole potential of the Drude model monolayer is 0.35V in excellent agreement with experimental estimates that range between 0.3 and 0.4V, whereas, a simulation using a nonpolarizable model significantly overestimates the potential with a calculated value of 0.8V. Induced polarization effects in the nonpolar region of the monolayer are found to buffer the residual positive lipid potential that results from competing polarization effects at the polar water/monolayer interface. These results, indicate the utility of the inclusion of many-body polarization effects in empirical force field models of lipids.
Local entanglement structure across a many-body localization transition
NASA Astrophysics Data System (ADS)
Bera, Soumya; Lakshminarayan, Arul
2016-04-01
Local entanglement between pairs of spins, as measured by concurrence, is investigated in a disordered spin model that displays a transition from an ergodic to a many-body localized phase in excited states. It is shown that the concurrence vanishes in the ergodic phase and becomes nonzero and increases in the many-body localized phase. This happen to be correlated with the transition in the spectral statistics from Wigner to Poissonian distribution. A scaling form is found to exist in the second derivative of the concurrence with the disorder strength. It also displays a critical value for the localization transition that is close to what is known in the literature from other measures. An exponential decay of concurrence with distance between spins is observed in the localized phase. Nearest neighbor spin concurrence in this phase is also found to be strongly correlated with the disorder configuration of on-site fields: nearly similar fields implying larger entanglement.
Combined coupled-cluster and many-body perturbation theories
NASA Astrophysics Data System (ADS)
Hirata, So; Fan, Peng-Dong; Auer, Alexander A.; Nooijen, Marcel; Piecuch, Piotr
2004-12-01
Various approximations combining coupled-cluster (CC) and many-body perturbation theories have been derived and implemented into the parallel execution programs that take into account the spin, spatial (real Abelian), and permutation symmetries and that are applicable to closed- and open-shell molecules. The implemented models range from the CCSD(T), CCSD[T], CCSD(2)T, CCSD(2)TQ, and CCSDT(2)Q methods to the completely renormalized (CR) CCSD(T) and CCSD[T] approaches, where CCSD (CCSDT) stands for the CC method with connected single and double (single, double, and triple) cluster operators, and subscripted or parenthesized 2, T, and Q indicate the perturbation order or the excitation ranks of the cluster operators included in the corrections. The derivation and computer implementation have been automated by the algebraic and symbolic manipulation program TENSOR CONTRACTION ENGINE (TCE). The TCE-synthesized subroutines generate the tensors with the highest excitation rank in a blockwise manner so that they need not be stored in their entirety, while enabling the efficient reuse of other precalculated intermediate tensors defined by prioritizing the memory optimization as well as operation minimization. Consequently, the overall storage requirements for the corrections due to connected triple and quadruple cluster operators scale as O(n4) and O(n6), respectively (n being a measure of the system size). For systems with modest multireference character of their wave functions, we found that the order of accuracy is CCSD
On the representation of many-body interactions in water
Medders, Gregory R.; Gotz, Andreas W.; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-09
Our recent work has shown that the many-body expansion of the interactionenergy can be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and long-range interactions at different orders is investigated by analyzing water potentials that treat the leading terms of the many-body expansion through implicit (i.e., TTM3-F and TTM4-F PESs) and explicit (i.e., WHBB and MB-pol PESs) representations. Moreover, it is found that explicit short-range representations of 2-body and 3-body interactions along with a physically correct incorporation of short- and long-range contributions are necessary for an accurate representationmore » of the waterinteractions from the gas to the condensed phase. Likewise, a complete many-body representation of the dipole moment surface is found to be crucial to reproducing the correct intensities of the infrared spectrum of liquid water.« less
Entangling qubit registers via many-body states of ultracold atoms
NASA Astrophysics Data System (ADS)
Melko, R. G.; Herdman, C. M.; Iouchtchenko, D.; Roy, P.-N.; Del Maestro, A.
2016-04-01
Inspired by the experimental measurement of the Rényi entanglement entropy in a lattice of ultracold atoms by Islam et al. [Nature (London) 528, 77 (2015), 10.1038/nature15750], we propose a method to entangle two spatially separated qubits using the quantum many-body state as a resource. Through local operations accessible in an experiment, entanglement is transferred to a qubit register from atoms at the ends of a one-dimensional chain. We compute the operational entanglement, which bounds the entanglement physically transferable from the many-body resource to the register, and discuss a protocol for its experimental measurement. Finally, we explore measures for the amount of entanglement available in the register after transfer, suitable for use in quantum information applications.
Many-Body Effects on Bandgap Shrinkage, Effective Masses, and Alpha Factor
NASA Technical Reports Server (NTRS)
Li, Jian-Zhong; Ning, C. Z.; Woo, Alex C. (Technical Monitor)
2000-01-01
Many-body Coulomb effects influence the operation of quantum-well (QW) laser diode (LD) strongly. In the present work, we study a two-band electron-hole plasma (EHP) within the Hatree-Fock approximation and the single plasmon pole approximation for static screening. Full inclusion of momentum dependence in the many-body effects is considered. An empirical expression for carrier density dependence of the bandgap renormalization (BGR) in an 8 nm GaAs/Al(0.3)G(4.7)As single QW will be given, which demonstrates a non-universal scaling behavior for quasi-two-dimension structures, due to size-dependent efficiency of screening. In addition, effective mass renormalization (EMR) due to momentum-dependent self-energy many-body correction, for both electrons and holes is studied and serves as another manifestation of the many-body effects. Finally, the effects on carrier density dependence of the alpha factor is evaluated to assess the sensitivity of the full inclusion of momentum dependence.
Many-body interactions and the melting of colloidal crystals
NASA Astrophysics Data System (ADS)
Dobnikar, J.; Chen, Y.; Rzehak, R.; von Grnberg, H. H.
2003-09-01
We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions among the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids. Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pair-interaction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions. If the salt concentration is high, we find configuration-independent pair forces of perfect Yukawa form with effective charges and screening constants that are in good agreement with well-established theories. At low added salt, however, the pair forces are Yukawa-type only at short distances with effective parameters that depend on the analyzed colloidal configuration. At larger distances, the pair-forces decay to zero much faster than they would following a Yukawa force law. Based on these findings, we suggest a simple model potential for colloids in suspension which has the form of a Yukawa potential, truncated after the first coordination shell of a colloid in a crystal. Using this potential in a one-component simulation, we find a melting line that shows good agreement with the one derived from the full Poisson-Boltzmann-Brownian-dynamics simulation.
Many-body-theory study of lithium photoionization
NASA Technical Reports Server (NTRS)
Chang, T. N.; Poe, R. T.
1975-01-01
A detailed theoretical calculation is carried out for the photoionization of lithium at low energies within the framework of Brueckner-Goldstone perturbational approach. In this calculation extensive use is made of the recently developed multiple-basis-set technique. Through this technique all second-order perturbation terms, plus a number of important classes of terms to infinite order, have been taken into account. Analysis of the results enables one to resolve the discrepancies between two previous works on this subject. The detailed calculation also serves as a test on the convergence of the many-body perturbation-expansion approach.
Novel approach to effective interactions for many-body calculations
NASA Astrophysics Data System (ADS)
Stetcu, Ionel; Barrett, Bruce R.; van Kolck, Ubirajara
2006-04-01
Even in the absence of exact solutions from QCD, effective field theories (EFT) provide a modern understanding of the nuclear forces at low energies. Based on a EFT which integrates out the pions as degrees of freedom (pionless theory), we present a new approach to the derivation of effective interactions suitable for many-body calculations by means of the no-core shell model. Such an approach can provide a consistent, order-by-order improvable method to obtain interactions tailored for the model spaces used in the many-body calculations, as well as the corresponding electromagnetic and weak operators. In this work, we concentrate on the description of two-body scattering observables in a restricted harmonic oscillator basis. I.S. and B.R.B. acknowledge partial support by NSF grant numbers PHY0070858 and PHY0244389. U.v.K. acknowledges partial support from DOE grant number DE-FG02-04ER41338 and from the Sloan Foundation.
Dynamical many-body phases of the parametrically driven, dissipative Dicke model
NASA Astrophysics Data System (ADS)
Chitra, R.; Zilberberg, O.
2015-08-01
Control and manipulation of quantum engineered systems allows for the utilization of time-dependent parametric modulations for accessing novel out-of-equilibrium phenomena. In the absence of such driving, the dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a parametric modulation of this coupling and discover a rich phase diagram as a function of the modulation strength. We find that in addition to the established normal and super-radiant phases, a new phase with pulsed superradiance, which we term dynamical normal phase, appears when the system is parametrically driven. Employing different methods, we characterize the different phases and the transitions between them. Specific heed is paid to the role of dissipation in determining the phase boundaries. Our analysis paves the road for the experimental study of dynamically stabilized phases of interacting light and matter.
Evolution of regulatory complexes: a many-body system
NASA Astrophysics Data System (ADS)
Nouemohammad, Armita; Laessig, Michael
2013-03-01
In eukaryotes, many genes have complex regulatory input, which is encoded by multiple transcription factor binding sites linked to a common function. Interactions between transcription factors and site complexes on DNA control the production of protein in cells. Here, we present a quantitative evolutionary analysis of binding site complexes in yeast. We show that these complexes have a joint binding phenotype, which is under substantial stabilizing selection and is well conserved within Saccharomyces paradoxus populations and between three species of Saccharomyces. At the same time, individual low-affinity sites evolve near-neutrally and show considerable affinity variation even within one population. Thus, functionality of and selection on regulatory complexes emerge from the entire cloud of sites, but cannot be pinned down to individual sites. Our method is based on a biophysical model, which determines site occupancies and establishes a joint affinity phenotype for binding site complexes. We infer a fitness landscape depending on this phenotype using yeast whole-genome polymorphism data and a new method of quantitative trait analysis. Our fitness landscape predicts the amount of binding phenotype conservation, as well as ubiquitous compensatory changes between sites in the cloud. Our results open a new avenue to understand the regulatory ``grammar'' of eukaryotic genomes based on quantitative evolution models. Carl-Icahn Laboratory, Washington Road, Princeton 08544 NJ
NASA Astrophysics Data System (ADS)
Burin, Alexander L.
2015-09-01
Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping V (R ) ∝R-α always leads to the localization breakdown in a thermodynamic limit of an infinite system at α <3 d /2 where d is a system dimension. The delocalization takes place due to the induced Ising interactions U (R ) ∝R-2 α of "extended" resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring α ≥2 d which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.
Many-body dispersion effects in the binding of adsorbates on metal surfaces.
Maurer, Reinhard J; Ruiz, Victor G; Tkatchenko, Alexandre
2015-09-14
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic-inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate-surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches. PMID:26374001
Extended slow dynamical regime near the many-body localization transition
NASA Astrophysics Data System (ADS)
Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
Many-body localization is characterized by a slow logarithmic growth of entanglement entropy after a global quantum quench while the local memory of an initial spin imbalance remains at infinite time. We address the dynamics in the delocalized ergodic regime, where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibium dynamics of the random-field Heisenberg chain is studied up to L = 28 sites, starting from an initially unantangled high-energy product state. With such a global quench protocol, we study the time evolution of the entanglement entropy, as well as the spin density imbalance in order to make contact with recent cold atom experiments. Within most of the delocalized phase, we unambiguously find a sub-ballistic entanglement growth S (t) ~t 1 / z with a disorder-dependent exponent z >= 1 , in contrast with the pure ballistic growth z = 1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t) ~t-ζ with a continuously varying disorder- dependent exponent ζ, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional metallic state where transport is sub-diffusive.
Many-body dispersion effects in the binding of adsorbates on metal surfaces
Maurer, Reinhard J.; Ruiz, Victor G.; Tkatchenko, Alexandre
2015-09-14
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic–inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate–surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches.
Topological and nematic ordered phases in many-body cluster-Ising models
NASA Astrophysics Data System (ADS)
Giampaolo, S. M.; Hiesmayr, B. C.
2015-07-01
We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size n +2 and is reached exactly when both interactions are equally weighted. For even n we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd n to a symmetry-protected topological ordered phase. Though complex, we are able to quantify the multiparticle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no n +1 -partite entanglement. This is possible since the nontrivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough (local) genuine n +2 -partite entanglement is built up. Due to their analytical solvableness the n -cluster-Ising models serve as a prototype for studying nontrivial-spin orderings, and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.
Many-body dispersion effects in the binding of adsorbates on metal surfaces
NASA Astrophysics Data System (ADS)
Maurer, Reinhard J.; Ruiz, Victor G.; Tkatchenko, Alexandre
2015-09-01
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic-inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate-surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches.
First-principles energetics of water clusters and ice: A many-body analysis
NASA Astrophysics Data System (ADS)
Gillan, M. J.; Alfè, D.; Bartók, A. P.; Csányi, G.
2013-12-01
Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
First-principles energetics of water clusters and ice: A many-body analysis
Gillan, M. J.; Alfè, D.; Thomas Young Centre, UCL, London WC1H 0AH; Department of Physics and Astronomy, UCL, London WC1E 6BT; Department of Earth Sciences, UCL, London WC1E 6BT ; Bartók, A. P.; Csányi, G.
2013-12-28
Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
Many-body tight-binding model for aluminum nanoparticles
Staszewska, Grazyna; Staszewski, Przemyslaw; Schultz, Nathan E.; Truhlar, Donald G.
2005-01-15
A new, parametrized many-body tight-binding model is proposed for calculating the potential energy surface for aluminum nanoparticles. The parameters have been fitted to reproduce the energies for a variety of aluminum clusters (Al{sub 2}, Al{sub 3}, Al{sub 4}, Al{sub 7}, Al{sub 13}) calculated recently by the PBE0/MG3 method as well as the experimental face-centered-cubic cohesive energy, lattice constant, and a small set of Al cluster ionization potentials. Several types of parametrization are presented and compared. The mean unsigned error per atom for the best model is less than 0.03 eV.
Relativistic many-body theory of atomic structures
Cheng, K.T.
1983-01-01
The main objective of this program is to improve our understanding of the effect of relativity and electron correlations on atomic processes. Current efforts include hyperfine structure (hfs) studies using the multiconfiguration Dirac-Fock (MCDF) technique. Atomic hfs are known to be sensitive to relativity and electron correlations, and provide important tests of relativistic atomic many-body theories. Preliminary results on the hfs of the 4f/sup 12/ /sup 3/H ground state of /sub 68/Er/sup 167/ are shown and are in good agreement with experiment. This shows that the MCDF technique can be an efficient and powerful method for atomic hfs studies. Further tests of this method are in progress. We are also studying the absorption spectra for Xe-like ions in the region of 4d ..-->.. nf, epsilonf transitions.
Reboredo, Fernando A.; Kim, Jeongnim
2014-02-21
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.
Another New Solvable Many-Body Model of Goldfish Type
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2012-07-01
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'') featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion of an arbitrary number N of unit-mass point-particles in a plane. The N (generally complex) values z_{n}( t) at time t of the N coordinates of these moving particles are given by the N eigenvalues of a time-dependent N× N matrix U( t) explicitly known in terms of the 2N initial data z_{n}( 0) and dot{z}_{n}(0) . This model comes in two different variants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''); for other special values of these parameters this property holds up to corrections vanishing exponentially as t→ ∞ (''asymptotic isochrony''). Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.
Electron-phonon coupling using many-body GW theory
NASA Astrophysics Data System (ADS)
Monserrat, Bartomeu; Vanderbilt, David
Electron-phonon coupling drives a plethora of phenomena, such as superconductivity in metals, or the temperature dependence of optical properties in semiconductors. There is increasing evidence that semi-local density functional theory (DFT) is not adequate for the description of electron-phonon coupling, and instead effects such as electronic correlation need to be included. Unfortunately, methods beyond semi-local DFT are computationally demanding, limiting the study of these phenomena. In this talk we will introduce the idea of ``thermal lines'', which can be used to explore the vibrational phase space of solids and molecules at small computational cost. In particular, we will describe how thermal lines can be exploited to calculate the temperature dependence of band structures beyond semi-local DFT, by using many-body GW theory, or by including the effects of spin-orbit coupling. We will present first-principles results showing the effects of electron correlation on the strength of electron-phonon coupling, and the effects of electron-phonon coupling on topological states of matter. Supported by Robinson College, Cambridge, and the Cambridge Philosophical Society.
Many-Body Approach to Mesons, Hybrids and Glueballs
NASA Astrophysics Data System (ADS)
Cotanch, Stephen R.; Llanes-Estrada, Felipe J.
2002-02-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is dynamically broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. We perform a comparative study of alternative many-body techniques for approximately diagonalizing H: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. We adequately describe the experimental meson and lattice glueball spectra and perform the first relativistic, three quasiparticle calculation for hybrid mesons. In general agreement with alternative theoretical approaches, we predict the lightest hybrid states near but above 2 GeV, indicating the two recently observed JPC = 1-+ exotics at 1.4 and 1.6 GeV are of a different, perhaps four quark, structure. We also detail a new isospin dependent interaction from q/line{q} color octet annihilation (analogous to ortho positronium) which splits I = 0 and I = 1 states.
From Discrete Breathers to Many Body Localization and Flatbands
NASA Astrophysics Data System (ADS)
Flach, Sergej
Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.
Approaching the complete-basis limit with a truncated many-body expansion
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2013-12-14
High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-ζ basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion–water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers.
Atomic many-body effects and Lamb shifts in alkali metals
NASA Astrophysics Data System (ADS)
Ginges, J. S. M.; Berengut, J. C.
2016-05-01
We present a detailed study of the radiative potential method [V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005), 10.1103/PhysRevA.72.052115], which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms and ions over the range 10 ≤Z ≤120 , where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s , p , and d waves over the series of alkali-metal atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many-body effects of core relaxation and second- and higher-order perturbation theory on the interaction of the valence electron with the core are calculated. The inclusion of many-body effects tends to increase the size of the shifts, with the enhancement particularly significant for d waves; for K to E119, the self-energy shifts for d waves are only an order of magnitude smaller than the s -wave shifts. It is shown that taking into account many-body effects is essential for an accurate description of the Lamb shift.
Equilibration properties of a disordered interacting open quantum system
NASA Astrophysics Data System (ADS)
van Nieuwenburg, Evert; Huber, Sebastian
The central question in the field of many body localization is if a closed interacting quantum system effectively thermalizes in the presence of disorder. However, any experimental test necessarily involves the opening of the ideally closed quantum system. Both from a fundamental point of view as well as for concrete experimental investigations of many body localization phenomena, a solid understanding of the effect of an attached bath is of significant importance. We study the equilibration properties of disordered interacting open quantum systems. On the one hand we consider the equilibration of such a many body localized system by coupling baths to the ends of a 1D spin chain. We find non-monotonous behaviour of the slowest relaxation time towards equilibrium. On the other hand, we take the bath itself to be a disordered interacting open quantum system and investigate the dephasing of a single qubit coupled to it. The model for the bath has a many body localization transition, affecting the dephasing of the single qubit.
Direct observation of many-body charge density oscillations in a two-dimensional electron gas.
Sessi, Paolo; Silkin, Vyacheslav M; Nechaev, Ilya A; Bathon, Thomas; El-Kareh, Lydia; Chulkov, Evgueni V; Echenique, Pedro M; Bode, Matthias
2015-01-01
Quantum interference is a striking manifestation of one of the basic concepts of quantum mechanics: the particle-wave duality. A spectacular visualization of this effect is the standing wave pattern produced by elastic scattering of surface electrons around defects, which corresponds to a modulation of the electronic local density of states and can be imaged using a scanning tunnelling microscope. To date, quantum-interference measurements were mainly interpreted in terms of interfering electrons or holes of the underlying band-structure description. Here, by imaging energy-dependent standing-wave patterns at noble metal surfaces, we reveal, in addition to the conventional surface-state band, the existence of an 'anomalous' energy band with a well-defined dispersion. Its origin is explained by the presence of a satellite in the structure of the many-body spectral function, which is related to the acoustic surface plasmon. Visualizing the corresponding charge oscillations provides thus direct access to many-body interactions at the atomic scale. PMID:26498368
Direct observation of many-body charge density oscillations in a two-dimensional electron gas
NASA Astrophysics Data System (ADS)
Sessi, Paolo; Silkin, Vyacheslav M.; Nechaev, Ilya A.; Bathon, Thomas; El-Kareh, Lydia; Chulkov, Evgueni V.; Echenique, Pedro M.; Bode, Matthias
2015-10-01
Quantum interference is a striking manifestation of one of the basic concepts of quantum mechanics: the particle-wave duality. A spectacular visualization of this effect is the standing wave pattern produced by elastic scattering of surface electrons around defects, which corresponds to a modulation of the electronic local density of states and can be imaged using a scanning tunnelling microscope. To date, quantum-interference measurements were mainly interpreted in terms of interfering electrons or holes of the underlying band-structure description. Here, by imaging energy-dependent standing-wave patterns at noble metal surfaces, we reveal, in addition to the conventional surface-state band, the existence of an `anomalous' energy band with a well-defined dispersion. Its origin is explained by the presence of a satellite in the structure of the many-body spectral function, which is related to the acoustic surface plasmon. Visualizing the corresponding charge oscillations provides thus direct access to many-body interactions at the atomic scale.
Many-body manifestation of interaction-free measurement: The Elitzur-Vaidman bomb
NASA Astrophysics Data System (ADS)
Zilberberg, Oded; Romito, Alessandro; Gefen, Yuval
2016-03-01
We consider an implementation of the Elitzur-Vaidman bomb experiment in a dc-biased electronic Mach-Zehnder interferometer with a leakage port on one of its arms playing the role of a "lousy bomb." Many-body correlations tend to screen out manifestations of interaction-free measurement. Analyzing the correlations between the current at the interferometer's drains and at the leakage port, we identify the limit where the originally proposed single-particle effect is recovered. Specifically, we find that in the regime of sufficiently diluted injected electron beam and short measurement times, effects of quantum-mechanical wave-particle duality emerge in the cross-current correlations.
Novel solvable extensions of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Calogero, F.; Iona, S.
2005-10-01
A novel solvable extension of the goldfish N-body problem is presented. Its Newtonian equations of motion read ζ̈n=2aζ\\dot nζn+2∑m =1,m≠nN(ζ\\dot n-aζn2)(ζ\\dot m-aζm2)/(ζn-ζm), n =1,…,N, where a is an arbitrary (nonvanishing) constant and the rest of the notation is self-evident. The isochronous version of this model is characterized by the Newtonian equations of motion ζ̈n-3iω\\zdot n-2ω2zn=2a(\\zdot n-iωzn)zn+2∑m =1,m≠nN(\\zdot n-iωzn-azn2)(\\zdot m-iωzm-azm2)/(zn-zm), n =1,…,N, where ω is an arbitrary positive constant and the points zn(t) move now necessarily in the complex z-plane. The generic solution of this second model is completely periodic with a period Tk=kT which is an integer multiple k (not larger than N!, indeed generally much smaller) of the basic period T =2π/ω and which is independent of the initial data (for sufficiently small, but otherwise arbitrary, changes of such data). These many-body models have an intriguing variety of equilibrium configurations (genuine: with no two particles sitting at the same place), but only for small values of N (N =2,3,4 for the first model, N =2,3,4,5 for the second). Other versions of these models are also discussed. The study of the behavior of the second, isochronous model around its equilibrium configurations yields some amusing diophantine results.
NASA Astrophysics Data System (ADS)
Krishtal, Alisa; Sinha, Debalina; Genova, Alessandro; Pavanello, Michele
2015-05-01
Subsystem density-functional theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to the computation of condensed phase systems, their excited states, and the evaluation of many-body interactions between the subsystems. As subsystem DFT is in principle an exact theory, any advance in this field can have a dual role. One is the possible applicability of a resulting method in practical calculations. The other is the possibility of shedding light on some quantum-mechanical phenomenon which is more easily treated by subdividing a supersystem into subsystems. An example of the latter is many-body interactions. In the discussion, we present some recent work from our research group as well as some new results, casting them in the current state-of-the-art in this review as comprehensively as possible.
Charge-dependent many-body exchange and dispersion interactions in combined QM/MM simulations.
Kuechler, Erich R; Giese, Timothy J; York, Darrin M
2015-12-21
Accurate modeling of the molecular environment is critical in condensed phase simulations of chemical reactions. Conventional quantum mechanical/molecular mechanical (QM/MM) simulations traditionally model non-electrostatic non-bonded interactions through an empirical Lennard-Jones (LJ) potential which, in violation of intuitive chemical principles, is bereft of any explicit coupling to an atom's local electronic structure. This oversight results in a model whereby short-ranged exchange-repulsion and long-ranged dispersion interactions are invariant to changes in the local atomic charge, leading to accuracy limitations for chemical reactions where significant atomic charge transfer can occur along the reaction coordinate. The present work presents a variational, charge-dependent exchange-repulsion and dispersion model, referred to as the charge-dependent exchange and dispersion (QXD) model, for hybrid QM/MM simulations. Analytic expressions for the energy and gradients are provided, as well as a description of the integration of the model into existing QM/MM frameworks, allowing QXD to replace traditional LJ interactions in simulations of reactive condensed phase systems. After initial validation against QM data, the method is demonstrated by capturing the solvation free energies of a series of small, chlorine-containing compounds that have varying charge on the chlorine atom. The model is further tested on the SN2 attack of a chloride anion on methylchloride. Results suggest that the QXD model, unlike the traditional LJ model, is able to simultaneously obtain accurate solvation free energies for a range of compounds while at the same time closely reproducing the experimental reaction free energy barrier. The QXD interaction model allows explicit coupling of atomic charge with many-body exchange and dispersion interactions that are related to atomic size and provides a more accurate and robust representation of non-electrostatic non-bonded QM/MM interactions. PMID:26696050
Charge-dependent many-body exchange and dispersion interactions in combined QM/MM simulations
NASA Astrophysics Data System (ADS)
Kuechler, Erich R.; Giese, Timothy J.; York, Darrin M.
2015-12-01
Accurate modeling of the molecular environment is critical in condensed phase simulations of chemical reactions. Conventional quantum mechanical/molecular mechanical (QM/MM) simulations traditionally model non-electrostatic non-bonded interactions through an empirical Lennard-Jones (LJ) potential which, in violation of intuitive chemical principles, is bereft of any explicit coupling to an atom's local electronic structure. This oversight results in a model whereby short-ranged exchange-repulsion and long-ranged dispersion interactions are invariant to changes in the local atomic charge, leading to accuracy limitations for chemical reactions where significant atomic charge transfer can occur along the reaction coordinate. The present work presents a variational, charge-dependent exchange-repulsion and dispersion model, referred to as the charge-dependent exchange and dispersion (QXD) model, for hybrid QM/MM simulations. Analytic expressions for the energy and gradients are provided, as well as a description of the integration of the model into existing QM/MM frameworks, allowing QXD to replace traditional LJ interactions in simulations of reactive condensed phase systems. After initial validation against QM data, the method is demonstrated by capturing the solvation free energies of a series of small, chlorine-containing compounds that have varying charge on the chlorine atom. The model is further tested on the SN2 attack of a chloride anion on methylchloride. Results suggest that the QXD model, unlike the traditional LJ model, is able to simultaneously obtain accurate solvation free energies for a range of compounds while at the same time closely reproducing the experimental reaction free energy barrier. The QXD interaction model allows explicit coupling of atomic charge with many-body exchange and dispersion interactions that are related to atomic size and provides a more accurate and robust representation of non-electrostatic non-bonded QM/MM interactions.
NASA Astrophysics Data System (ADS)
Carmele, Alexander; Heyl, Markus; Kraus, Christina; Dalmonte, Marcello
2015-11-01
We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occurring in the bulk. In particular, for pure loss dynamics we find a universal exponent α ≃2 /3 . We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.
Dynamical and statistical modelling of many body collisions Part I: Scattering
NASA Astrophysics Data System (ADS)
Agbormbai, A. A.
2001-08-01
Although rarefied gas dynamics has traditionally rested on the dilute gas assumption, which presupposes that only binary collisions and single-body gas surface interactions occur, expressions for many-body collision rates and for many-body gas surface interaction (GSI) rates seem to suggest that at lesser heights the dilute gas assumption is not valid. In particular, in the pure rarefied regime, two-body GSIs and some three-body interactions occur whereas, in the transition regime into continuum flow, four body collisions and four body GSIs occur. In this paper I formulate many body collisions using dynamical and statistical modelling. I show that the results of binary collisions can be useful in formulating many body collisions. In particular, I show that the equations of motion of a many body system can be recast into the equations of motion of a number of reduced particles which scatter in space as well as exchange energy with one another and with the center of mass of the system. For N-interacting bodies there are N-1 reduced particles. In this paper I focus on the scattering of the reduced particles. For two-body collisions the scattering of the single reduced particle is confined to a single plane. However, for many body collisions the equations of motion show that the scattering of each reduced particle occurs in space. Hence, there is an in-plane deflection as well as an out-of-plane deflection. I calculate each deflection using the two-body formula, but with important modifications to account for the resolution of the intermolecular potential into in-plane and out-of-plane components. The magnitude of the potential is also adjusted to take account of coefficients derived from the equations of motion. I also propose an approximate model, which computes the in-plane deflection as in binary collisions but computes the out-of-plane deflection using a statistical model based on reciprocity or detailed balance. The models are designed for Direct Simulation Monte Carlo computations of rarefied gas phenomena.
Importance of many-body correlations in glass transition: An example from polydisperse hard spheres
NASA Astrophysics Data System (ADS)
Leocmach, Mathieu; Russo, John; Tanaka, Hajime
2013-03-01
Most of the liquid-state theories, including glass-transition theories, are constructed on the basis of two-body density correlations. However, we have recently shown that many-body correlations, in particular, bond orientational correlations, play a key role in both the glass transition and the crystallization transition. Here we show, with numerical simulations of supercooled polydisperse hard spheres systems, that the length-scale associated with any two-point spatial correlation function does not increase toward the glass transition. A growing length-scale is instead revealed by considering many-body correlation functions, such as correlators of orientational order, which follows the length-scale of the dynamic heterogeneities. Despite the growing of crystal-like bond orientational order, we reveal that the stability against crystallization with increasing polydispersity is due to an increasing population of icosahedral arrangements of particles. Our results suggest that, for this type of systems, many-body correlations are a manifestation of the link between the vitrification and the crystallization phenomena. Whether a system is vitrified or crystallized can be controlled by the degree of frustration against crystallization, polydispersity in this case.
Encoding the structure of many-body localization with matrix product operators
NASA Astrophysics Data System (ADS)
Pekker, David; Clark, Bryan K.
2015-03-01
Anderson insulators are non-interacting disordered systems which have localized single particle eigenstates. The interacting analogue of Anderson insulators are the Many-Body Localized (MBL) phases. The natural language for representing the spectrum of the Anderson insulator is that of product states over the single-particle modes. We show that product states over Matrix Product Operators of small bond dimension is the corresponding natural language for describing the MBL phases. In this language all of the many-body eigenstates are encode by Matrix Product States (i.e. DMRG wave function) consisting of only two sets of low bond-dimension matrices per site: the Gi matrix corresponding to the local ground state on site i and the Ei matrix corresponding to the local excited state. All 2 n eigenstates can be generated from all possible combinations of these matrices.
Flow equation approach to one-body and many-body localization
NASA Astrophysics Data System (ADS)
Quito, Victor; Bhattacharjee, Paraj; Pekker, David; Refael, Gil
2014-03-01
We study one-body and many-body localization using the flow equation technique applied to spin-1/2 Hamiltonians. This technique, first introduced by Wegner, allows us to exact diagonalize interacting systems by solving a set of first-order differential equations for coupling constants. Besides, by the flow of individual operators we also compute physical properties, such as correlation and localization lengths, by looking at the flow of probability distributions of couplings in the Hilbert space. As a first example, we analyze the one-body localization problem written in terms of spins, the disordered XY model with a random transverse field. We compare the results obtained in the flow equation approach with the diagonalization in the fermionic language. For the many-body problem, we investigate the physical properties of the disordered XXZ Hamiltonian with a random transverse field in the z-direction.
Kohn-Sham density-functional theory and renormalization of many-body perturbation expansions
NASA Astrophysics Data System (ADS)
Valiev, Marat
1998-03-01
Numerous practical applications provide strong evidence that despite its simplicity and crude approximations, density-functional theory leads to a rather accurate description of ground state properties of various condensed matter systems. Although well documented numerically, to our knowledge a theoretical explanation of the accuracy of density-functional theory has not been given. This issue is clarified in this work by demonstrating that density-functional theory represents a particular renormalization procedure of a many-body perturbation expansion. In other words, it is shown that density-functional theory is a many-body perturbation theory whose convergence properties have been optimized. The realization of this fact brings new meaning into density-functional theory and explains the success of density-functional based calculations. For more information go to http://alchemy.ucsd.edu/marat/ .
Recent development of complex scaling method for many-body resonances and continua in light nuclei
NASA Astrophysics Data System (ADS)
Myo, Takayuki; Kikuchi, Yuma; Masui, Hiroshi; Katō, Kiyoshi
2014-11-01
The complex scaling method (CSM) is a useful similarity transformation of the Schrödinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the L2 basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lines. Non-resonant continuum states are also obtained with the discretized eigenvalues on the rotated branch cuts. Using these complex eigenvalues and eigenstates in CSM, we construct the extended completeness relations and Green's functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented.
Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition
NASA Astrophysics Data System (ADS)
Devakul, Trithep; Singh, Rajiv
We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies. Work based on Phys. Rev. Lett. 115, 187201.
Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition
NASA Astrophysics Data System (ADS)
Devakul, Trithep; Singh, Rajiv R. P.
2015-10-01
We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.
Quantum Simulation for Open-System Dynamics
NASA Astrophysics Data System (ADS)
Wang, Dong-Sheng; de Oliveira, Marcos Cesar; Berry, Dominic; Sanders, Barry
2013-03-01
Simulations are essential for predicting and explaining properties of physical and mathematical systems yet so far have been restricted to classical and closed quantum systems. Although forays have been made into open-system quantum simulation, the strict algorithmic aspect has not been explored yet is necessary to account fully for resource consumption to deliver bounded-error answers to computational questions. An open-system quantum simulator would encompass classical and closed-system simulation and also solve outstanding problems concerning, e.g. dynamical phase transitions in non-equilibrium systems, establishing long-range order via dissipation, verifying the simulatability of open-system dynamics on a quantum Turing machine. We construct an efficient autonomous algorithm for designing an efficient quantum circuit to simulate many-body open-system dynamics described by a local Hamiltonian plus decoherence due to separate baths for each particle. The execution time and number of gates for the quantum simulator both scale polynomially with the system size. DSW funded by USARO. MCO funded by AITF and Brazilian agencies CNPq and FAPESP through Instituto Nacional de Ciencia e Tecnologia-Informacao Quantica (INCT-IQ). DWB funded by ARC Future Fellowship (FT100100761). BCS funded by AITF, CIFAR, NSERC and USARO.
TRIQS: A toolbox for research on interacting quantum systems
NASA Astrophysics Data System (ADS)
Parcollet, Olivier; Ferrero, Michel; Ayral, Thomas; Hafermann, Hartmut; Krivenko, Igor; Messio, Laura; Seth, Priyanka
2015-11-01
We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it.
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2016-03-01
A fully many-body localized (FMBL) quantum disordered system is characterized by the emergence of an extensive number of local conserved operators that prevents the relaxation towards thermal equilibrium. These local conserved operators can be seen as the building blocks of the whole set of eigenstates. In this paper, we propose to construct them explicitly via block real-space renormalization. The principle is that each renormalization group step diagonalizes the smallest remaining blocks and produces a conserved operator for each block. The final output for a chain of N spins is a hierarchical organization of the N conserved operators with ≤ft(\\frac{\\ln N}{\\ln 2}\\right) layers. The system size nature of the conserved operators of the top layers is necessary to describe the possible long-range order of the excited eigenstates and the possible critical points between different FMBL phases. We discuss the similarities and the differences with the strong disorder RSRG-X method that generates the whole set of the 2 N eigenstates via a binary tree of N layers. The approach is applied to the long-range quantum spin-glass Ising model, where the constructed excited eigenstates are found to be exactly like ground states in another disorder realization, so that they can be either in the paramagnetic phase, in the spin-glass phase or critical.
Many-body critical Casimir interactions in colloidal suspensions.
Hobrecht, Hendrik; Hucht, Alfred
2015-10-01
We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the Z(2) symmetry of the system is broken by the particles. We present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions. PMID:26565248
Many-body critical Casimir interactions in colloidal suspensions
NASA Astrophysics Data System (ADS)
Hobrecht, Hendrik; Hucht, Alfred
2015-10-01
We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the Z2 symmetry of the system is broken by the particles. We present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions.
Many-body approach for quartet condensation in strong coupling
Sogo, Takaaki; Roepke, Gerd; Schuck, Peter
2010-06-15
The theory for condensation of higher fermionic clusters is developed. Fully self-consistent nonlinear equations for the quartet order parameter in strongly coupled fermionic systems are established and solved. The breakdown of the quasiparticle picture is pointed out. Derivation of numerically tractable approximation is described. The momentum projected factorization ansatz for the order parameter is employed. As a definite example, the condensation of alpha particles in nuclear matter is worked out.
The relativistic many body problem with an oscillator interaction
NASA Technical Reports Server (NTRS)
Moshinsky, Marcos
1995-01-01
We start with the total energy E for a system of three scalar relativistic particles that, because of Einstein's relation, will have square roots of functions of the momenta. By taking powers of this relation, we finally get a fourth degree polynomial in E(exp 2), where the square roots have disappeared, and which we can convert into a type of Schroedinger equation. To be in the center of mass frame we pass to Jocobi momenta and then replace them by creation and annihilation operators. We thus get an equation in terms of the generators of a U(2) group, which, in principle, we can solve in an elementary way. Finally, we rewrite our equation in a Poincare invariant form.
Nonperturbative dynamical many-body theory of a Bose-Einstein condensate
Gasenzer, Thomas; Berges, Juergen; Schmidt, Michael G.; Seco, Marcos
2005-12-15
A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The nonperturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory, and 'off-shell' effects that are not captured by the Gross-Pitaevskii equation. This is relevant to account for the dynamics of, e.g., strongly interacting quantum gases atoms near a scattering resonance, or of one-dimensional Bose gases in the Tonks-Girardeau regime. We apply the theory to a homogeneous ultracold Bose gas in one spatial dimension. Considering the time evolution of an initial state far from equilibrium we show that it quickly evolves to a nonequilibrium quasistationary state and discuss the possibility to attribute an effective temperature to it. The approach to thermal equilibrium is found to be extremely slow.
Non-perturbative approaches to problems in strongly-correlated many-body physics
NASA Astrophysics Data System (ADS)
Ma, Seungwook
The physics of strongly-correlated many-body systems pose formidable theoretical challenges. Methods based on perturbation theory break down due to the lack of a small parameter. This leads generically to the closure problem in a diagramatic expansion. In this thesis, we consider two such problems. The first involves the Mott insulator, a remarkable example of strong correlation effects among electrons leading to an insulating phase of what would otherwise be a metal. Of particular interest is the case when the ground state breaks neither the global rotational symmetry of the electronic spins nor the spatial symmetries of the lattice. Here the combination of strong coupling and quantum fluctuations leads to novel ground states with purely quantum mechanical origins. The second problem involves the statistics of dynamical systems. Although a set of nonlinear differential equations is deterministic and has a unique solution, it may be unstable to small triggering disturbances. Despite the unpredictability of individual trajectories, there may be reproducible and smoothly varying statistical properties. General methods to access directly statistical quantities are then necessary. In Part I of this thesis, we take the pragmatic view that the basic physics of spin liquids is contained in the one-band Hubbard model. For large on-site Coulomb repulsion, U → infinity, we consider the Heisenberg limit at half-filling and include possible subleading exchange anisotropies of the Dzyaloshinskii-Moriya (DM) type. The work is motivated by two experimental realizations of layered spin-1/2 antiferromagnets. The first is Cs2CuCl4 where the spins reside on a spatially anisotropic triangular lattice. The second is ZnCu3(OH)6Cl2, called Herbertsmithite. Here, the spins reside on a spatially isotropic kagome lattice. Both are rare candidate materials in the search for spin liquid physics in two dimensions. To interpret experimentally measured quantities, we exactly diagonalize the Hamiltonian on small clusters. In addition, we utilize Gutzwiller-projected mean field theory to test whether various spin liquid states may be realized in nature. In Part II of this thesis, we apply the method of Hopf to low dimensional toy models of turbulence. A well-known example is the first-order system of three coupled nonlinear equations invented by Lorenz. The motivation was to find a simple model, amenable to fast numerical evaluation and capturing essential difficulties found in long-term weather prediction. In the hope of developing a statistical understanding of the Navier-Stokes equations, Hopf pioneered a functional integral method. The Hopf equations are in terms of a characteristic functional that determines the full time-independent problem and is equivalent to knowledge of the exact probability distribution. In our discussion, we focus on a simple chaotic dynamical system introduced by Orszag and McLaughlin and determine the exact Hopf characteristic functional.
Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
NASA Astrophysics Data System (ADS)
Bihun, Oksana; Calogero, Francesco
2013-10-01
The class of solvable many-body problems ''of goldfish type'' is extended by including (the additional presence of) three-body forces. The solvable N-body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary ''coupling constants''. Restrictions on these constants are identified which cause these systems - or appropriate variants of them - to be isochronous or asymptotically isochronous, i.e. all their solutions to be periodic with a fixed period (independent of the initial data) or to have this property up to contributions vanishing exponentially as t→ ∞.
Liquid-gas phase transition in nuclear matter from realistic many-body approaches
Rios, A.; Polls, A.; Ramos, A.; Muether, H.
2008-10-15
The existence of a liquid-gas phase transition for hot nuclear systems at subsaturation densities is a well-established prediction of finite-temperature nuclear many-body theory. In this paper, we discuss for the first time the properties of such a phase transition for homogeneous nuclear matter within the self-consistent Green's function approach. We find a substantial decrease of the critical temperature with respect to the Brueckner-Hartree-Fock approximation. Even within the same approximation, the use of two different realistic nucleon-nucleon interactions gives rise to large differences in the properties of the critical point.
An effective many-body theory for strongly interacting polar molecules
NASA Astrophysics Data System (ADS)
Wang, Daw-Wei
2008-05-01
We derive a general, effective many-body theory for bosonic polar molecules in the strong interaction regime, which cannot be correctly described by previous theories within the first Born approximation. The effective Hamiltonian has additional interaction terms, which surprisingly reduce the anisotropic features of the condensate profile near the shape resonance regime. In a two-dimensional (2D) system with the dipole moment perpendicular to the plane, we find that the phonon dispersion scales as \\sqrt{\\vert{\\bf p}\\vert} in the low-momentum (p) limit, showing the same low energy properties as a 2D charged Bose gas with Coulomb (1/r) interactions.
Sorting quantum systems efficiently.
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) - which direct photons according to their polarization - and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Sorting quantum systems efficiently
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Hilbert-space localization in closed quantum systems
NASA Astrophysics Data System (ADS)
Cohen, Doron; Yukalov, Vyacheslav I.; Ziegler, Klaus
2016-04-01
Quantum localization within an energy shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space Anderson localization and its many-body Fock-space version. We use the term Hilbert-space localization in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state and on the strength of the many-body interactions using a recursive projection method.
Quantum coherence and correlations in quantum system
Xi, Zhengjun; Li, Yongming; Fan, Heng
2015-01-01
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice
NASA Astrophysics Data System (ADS)
Yi, W.; Diehl, S.; Daley, A. J.; Zoller, P.
2012-05-01
We discuss the preparation of many-body states of cold fermionic atoms in an optical lattice via controlled dissipative processes induced by coupling the system to a reservoir. Based on a mechanism combining Pauli blocking and phase locking between adjacent sites, we construct complete sets of jump operators describing coupling to a reservoir that leads to dissipative preparation of pairing states for fermions with various symmetries in the absence of direct inter-particle interactions. We discuss the uniqueness of these states, and demonstrate it with small-scale numerical simulations. In the late-time dissipative dynamics, we identify a ‘dissipative gap’ that persists in the thermodynamic limit. This gap implies exponential convergence of all many-body observables to their steady-state values. We then investigate how these pairing states can be used as a starting point for the preparation of the ground state of the Fermi-Hubbard Hamiltonian via an adiabatic state preparation process also involving the parent Hamiltonian of the pairing state. We also provide a proof-of-principle example for implementing these dissipative processes and the parent Hamiltonians of the pairing states, based on 171Yb atoms in optical lattice potentials.
Excitonic effects in GeC hybrid: Many-body Green's function calculations
NASA Astrophysics Data System (ADS)
Drissi, L. B.; Ramadan, F. Z.
2015-11-01
Many-body effects on the electronic and optical absorption properties of a GeC sheet are studied by means of first principle many-body Green's function and Bethe-Salpeter equation formalism. The absence of soft modes in the phonon-spectrum indicates the stability of the system. The inclusion of quasiparticle corrections increases significantly the band gap. The local field effects induce significant change in the absorption spectra for the out-plane polarization rendering the GeC monolayer transparent below 7 eV. The excitonic effects are significant on the optical absorption properties. A detailed analysis of the spectrum shows a strong binding energy of 1.82 eV assigned to the lowest-energy bound excitons that is characterized by an effective mass of 1.68 m0 and a Bohr radius of 2 Å. The results of this study hold the promise for potential applications of the GeC hybrid in optoelectronics.
Chmela, Jiří; Harding, Michael E; Matioszek, Dimitri; Anson, Christopher E; Breher, Frank; Klopper, Wim
2016-01-01
In computational chemistry, non-additive and cooperative effects can be defined in terms of a (differential) many-body expansion of the energy or any other physical property of the molecular system of interest. One-body terms describe energies or properties of the subsystems, two-body terms describe non-additive but pairwise contributions and three-body as well as higher-order terms can be interpreted as a measure for cooperativity. In the present article, this concept is applied to the analysis of ultraviolet/visible (UV/Vis) spectra of homotrinuclear transition-metal complexes by means of a many-body expansion of the change in the spectrum induced by replacing each of the three transition-metal ions by another transition-metal ion to yield a different homotrinuclear transition-metal complex. Computed spectra for the triangulo-complexes [M3 {Si(mt(Me) )3}2] (M=Pd/Pt, mt(Me) =methimazole) and tritopic triphenylene-based N-heterocyclic carbene Rh/Ir complexes illustrate the concept, showing large and small differential three-body cooperativity, respectively. PMID:26443262
Controlling many-body states by the electric-field effect in a two-dimensional material
NASA Astrophysics Data System (ADS)
Li, L. J.; O'Farrell, E. C. T.; Loh, K. P.; Eda, G.; Özyilmaz, B.; Castro Neto, A. H.
2016-01-01
To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially modulated electronic states are fundamental to the appearance of two-dimensional superconductivity.
Controlling many-body states by the electric-field effect in a two-dimensional material.
Li, L J; O'Farrell, E C T; Loh, K P; Eda, G; Özyilmaz, B; Castro Neto, A H
2016-01-14
To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially modulated electronic states are fundamental to the appearance of two-dimensional superconductivity. PMID:26700810
NASA Astrophysics Data System (ADS)
Ginges, J. S. M.; Berengut, J. C.
2016-05-01
We calculate vacuum polarization corrections to the binding energies in neutral alkali atoms Na through to the superheavy element E119. We employ the relativistic Hartree–Fock method to demonstrate the importance of relaxation of the electronic core and the correlation potential method to study the effects of second and higher orders of perturbation theory. These many-body effects are sizeable for all orbitals, though particularly important for orbitals with angular momentum quantum number l\\gt 0. The orders of magnitude enhancement for d waves produces shifts that, for Rb and the heavier elements, are larger than those for p waves and only an order of magnitude smaller than the s-wave shifts. The many-body enhancement mechanisms that operate for vacuum polarization apply also to the larger self-energy corrections.
Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid.
Dóra, Balázs; Pollmann, Frank; Fortágh, József; Zaránd, Gergely
2013-07-26
We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry. PMID:23931387
Many-Body Localization in the Presence of a Single-Particle Mobility Edge
NASA Astrophysics Data System (ADS)
Modak, Ranjan; Mukerjee, Subroto
2015-12-01
In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.
Many-body Green's function study of coumarins for dye-sensitized solar cells
NASA Astrophysics Data System (ADS)
Faber, Carina; Duchemin, Ivan; Deutsch, Thierry; Blase, Xavier
2012-10-01
We study within the many-body Green's function GW and Bethe-Salpeter formalisms the excitation energies of several coumarin dyes proposed as an efficient alternative to ruthenium complexes for dye-sensitized solar cells. Due to their internal donor-acceptor structure, these chromophores present low-lying excitations showing a strong intramolecular charge-transfer character. We show that combining GW and Bethe-Salpeter calculations leads to charge-transfer excitation energies and oscillator strengths in excellent agreement with reference range-separated functional studies or coupled-cluster calculations. The present results confirm the ability of this family of approaches to describe accurately Frenkel and charge-transfer photo-excitations in both extended and finite size systems without any system-dependent adjustable parameter, paving the way to the study of dye-sensitized semiconducting surfaces.
Quantum electromechanical systems
NASA Astrophysics Data System (ADS)
Milburn, Gerard J.; Polkinghorne, Rodney
2001-11-01
We discuss the conditions under which electromechanical systems, fabricated on a sub micron scale, require a quantum description. We illustrate the discussion with the example of a mechanical electroscope for which the resonant frequency of a cantilever changes in response to a local charge. We show how such devices may be used as a quantum noise limited apparatus for detection of a single charge or spin with applications to quantum computing.
Many-body processes in black and gray matter-wave solitons
NASA Astrophysics Data System (ADS)
Krönke, Sven; Schmelcher, Peter
2015-05-01
We perform a comparative beyond-mean-field study of black and gray solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized density-engineering potential is developed and employed together with phase imprinting to cleanly initialize gray solitons. By means of ab initio simulations with the multiconfiguration time-dependent Hartree method for bosons, we demonstrate that quantum fluctuations limit the lifetime of the soliton contrast, which increases with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of gray solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analyzed in detail. Finally, the role of phase imprinting for the many-body dynamics is illuminated and additional nonlocal correlations in pairs of counterpropagating gray solitons are observed.
Relativistic and Field Theoretic Effects in the Nuclear Many-Body Problem.
NASA Astrophysics Data System (ADS)
Poorakkiat, Chaisingh
Field theoretic effects of a nucleon of an oxygen -17 have been studied. A computational scheme involving sigma and omega mesons has been set up. It employs the Furry picture of quantum field theory along with an introduction of vector and scalar Woods-Saxon potentials. Use of an adiabatic switching on an interaction leads to an energy shift in form of a symmetric Gell-Mann and Low formula which contains the S matrix. The S matrix allows an expansion in terms of Feynman diagrams which in turn enables us to write a perturbative series analogous to that in many-body perturbation theory. Retardation effects and the first-order energy correction E_{1} of two valence states, 1d_{5/2} and 2s_{1/2}, have been calculated from the diagrams. The self-energy of the 1s _{1/2} state is investigated along with the use of a renormalization technique. The retardation effects are small in the order of 10 kev while the self-energy and E_{1} corrections are big in the order of 700 and 10 Mev respectively.
Many body effects study of electronic & optical properties of silicene-graphene hybrid
NASA Astrophysics Data System (ADS)
Drissi, L. B.; Ramadan, F. Z.
2015-04-01
Using first principles many-body calculations method, we study electronic and optical properties of 2D silicene-graphene hybrid. Based on phonon-spectrum calculations, we show the absence of soft modes indicating the stability of the system. We also calculate the band gap in both the absence and the presence of quasiparticle corrections. The analysis of optical absorption spectra and the correlation in real space between the excited electron-hole states reveals that the excitonic effects in silicene-graphene hybrid are significant and leads to strong bound excitons. The first active exciton is characterized by a binding energy of 0.81 eV, an effective mass 0.41m0 and a Bohr radius of 2.78 Å. The results of this work make silicene-graphene hybrid a promising candidate for optoelectronic applications.
NASA Astrophysics Data System (ADS)
Karrasch, C.; Moore, J. E.
2015-09-01
We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over 104 samples for lattices as large as 105 sites. We identify regimes in which non-Ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In the presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.
Electronic excitations of bulk LiCl from many-body perturbation theory
Jiang, Yun-Feng; Wang, Neng-Ping; Rohlfing, Michael
2013-12-07
We present the quasiparticle band structure and the optical excitation spectrum of bulk LiCl, using many-body perturbation theory. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap is 9.5 eV, which is in good agreement with the experimental result of 9.4 eV. And the calculated optical absorption spectrum, which contains an exciton peak at 8.8 eV and a resonant-exciton peak at 9.8 eV, is also in good agreement with experimental data.
Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry
NASA Astrophysics Data System (ADS)
Knap, Michael; Kantian, Adrian; Giamarchi, Thierry; Bloch, Immanuel; Lukin, Mikhail D.; Demler, Eugene
2013-10-01
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
Many-body microhydrodynamics of colloidal particles with active boundary layers
NASA Astrophysics Data System (ADS)
Singh, Rajesh; Ghose, Somdeb; Adhikari, R.
2015-06-01
Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.
Colloquium: Non-Markovian dynamics in open quantum systems
NASA Astrophysics Data System (ADS)
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of non-Markovian quantum dynamics are also briefly discussed.
The dimensionality reduction at surfaces as a playground for many-body and correlation effects
NASA Astrophysics Data System (ADS)
Tejeda, A.; Michel, E. G.; Mascaraque, A.
2013-03-01
Low-dimensional systems have always deserved attention due to the peculiarity of their physics, which is different from or even at odds with three-dimensional expectations. This is precisely the case for many-body effects, as electron-electron correlation or electron-phonon coupling are behind many intriguing problems in condensed matter physics. These interesting phenomena at low dimensions can be studied in one of the paradigms of two dimensionality—the surface of crystals. The maturity of today's surface science techniques allows us to perform thorough experimental studies that can be complemented by the current strength of state-of-the-art calculations. Surfaces are thus a natural two-dimensional playground for studying correlation and many-body effects, which is precisely the object of this special section. This special section presents a collection of eight invited articles, giving an overview of the current status of selected systems, promising techniques and theoretical approaches for studying many-body effects at surfaces and low-dimensional systems. The first article by Hofmann investigates electron-phonon coupling in quasi-free-standing graphene by decoupling graphene from two different substrates with different intercalating materials. The following article by Kirschner deals with the study of NiO films by electron pair emission, a technique particularly well-adapted for studying high electron correlation. Bovensiepen investigates electron-phonon coupling via the femtosecond time- and angle-resolved photoemission spectroscopy technique. The next article by Malterre analyses the phase diagram of alkalis on Si(111):B and studies the role of many-body physics. Biermann proposes an extended Hubbard model for the series of C, Si, Sn and Pb adatoms on Si(111) and obtains the inter-electronic interaction parameters by first principles. Continuing with the theoretical studies, Bechstedt analyses the influence of on-site electron correlation in insulating antiferromagnetic surfaces. Ortega reports on the gap of molecular layers on metal systems, where the metal-organic interaction affects the organic gap through correlation effects. Finally, Cazalilla presents a study of the phase diagram of one-dimensional atoms or molecules displaying a Kondo-exchange interaction with the substrate. Acknowledgments The editors are grateful to all the invited contributors to this special section of Journal of Physics: Condensed Matter. We also thank the IOP Publishing staff for handling the administrative matters and the refereeing process. Correlation and many-body effects at surfaces contents The dimensionality reduction at surfaces as a playground for many-body and correlation effectsA Tejeda, E G Michel and A Mascaraque Electron-phonon coupling in quasi-free-standing grapheneJens Christian Johannsen, Søren Ulstrup, Marco Bianchi, Richard Hatch, Dandan Guan, Federico Mazzola, Liv Hornekær, Felix Fromm, Christian Raidel, Thomas Seyller and Philip Hofmann Exploring highly correlated materials via electron pair emission: the case of NiO/Ag(100)F O Schumann, L Behnke, C H Li and J Kirschner Coherent excitations and electron-phonon coupling in Ba/EuFe2As2 compounds investigated by femtosecond time- and angle-resolved photoemission spectroscopyI Avigo, R Cortés, L Rettig, S Thirupathaiah, H S Jeevan, P Gegenwart, T Wolf, M Ligges, M Wolf, J Fink and U Bovensiepen Understanding the insulating nature of alkali-metal/Si(111):B interfacesY Fagot-Revurat, C Tournier-Colletta, L Chaput, A Tejeda, L Cardenas, B Kierren, D Malterre, P Le Fèvre, F Bertran and A Taleb-Ibrahimi What about U on surfaces? Extended Hubbard models for adatom systems from first principlesPhilipp Hansmann, Loïg Vaugier, Hong Jiang and Silke Biermann Influence of on-site Coulomb interaction U on properties of MnO(001)2 × 1 and NiO(001)2 × 1 surfacesA Schrön, M Granovskij and F Bechstedt On the organic energy gap problemF Flores, E Abad, J I Martínez, B Pieczyrak and J Ortega Easy-axis ferromagnetic chain on a metallic surfaceMiguel A Cazalilla
Quantum phase transitions in frustrated magnetic systems
NASA Astrophysics Data System (ADS)
Wölfle, P.; Schmitteckert, P.
2015-07-01
We review our recent work on quantum phase transitions in frustrated magnetic systems. In the first part a Pseudo Fermion Functional Renormalization Group (PFFRG) method is presented. By using an exact representation of spin 1/2 operators in terms of pseudofermions a quantum spin Hamiltonian may be mapped onto an interacting fermion system. For the latter an FRG treatment is employed. The results for the J1-J2 model and similar models of frustrated interaction show phase diagrams in agreement with those obtained by other methods, but give more detailed information on the nature of correlations, in particular in the non-magnetic phases. Applications of PFFRG to geometrically frustrated systems and to highly anisotropic Kitaev type models are also reported. In the second part the derivation of quantum spin models from the microscopic many-body Hamiltonian is discussed. The results for multiband systems with strong spin-orbit interaction encountered in the iridates class of compounds are shown to resolve some of the questions posed by experiment.
Vibrational modes in the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Daily, Kevin; Greene, Chris H.
The hyperspherical adiabatic technique is more familiar to atomic and nuclear few-body systems, but can also be applied with high accuracy to the many-body quantum Hall problem. This technique reformulates the Schrödinger equation for N electrons into hyperspherical coordinates, which, after extracting the trivial center of mass, describes the system in terms of a single global size coordinate known as the hyperradius R, and 2 N - 3 remaining internal angular coordinates. The solutions are approximately separable in the hyperradial coordinate, and solutions in the system are found by treating the hyperradius as an adiabatic coordinate. The approximate separability of the wave functions in this coordinate suggests the presence of hyperradial vibrational modes which are not described in conventional theories. The vibrationally excited states share the internal geometry of their quantum Hall ground states, and their excitation frequencies may vary with the number of participating particles or the strength of the confinement. We plan to discuss the features of these vibrational modes and their possible detection in quantum Hall systems. NSF.
Lyapunov control on quantum systems
NASA Astrophysics Data System (ADS)
Wang, L. C.; Yi, X. X.
2014-12-01
We review the scheme of quantum Lyapunov control and its applications into quantum systems. After a brief review on the general method of quantum Lyapunov control in closed and open quantum systems, we apply it into controlling quantum states and quantum operations. The control of a spin-1/2 quantum system, driving an open quantum system into its decoherence free subspace (DFS), constructing single qubit and two-qubit logic gates are taken to illustrate the scheme. The optimalization of the Lyapunov control is also reviewed in this article.
Many-body effects in a semiconductor microcavity laser: Experiment and theory
Crawford, M.H.; Choquette, K.D.; Chow, W.W.; Schneider, R.P. Jr.
1996-07-01
Many-body effects are observed in the threshold properties of selectively oxidized vertical-cavity surface-emitting lasers. These microcavity lasers represent the state-of-the-art in low threshold semiconductor injection lasers.
Irregular many-body dynamics of spinor Bose-Einstein condensates in an optical lattice.
Chong, Guishu; Borondo, F
2008-07-01
The classical and quantum irregular spin dynamics of atomic spinor Bose-Einstein condensates in an optical lattice, where light-induced and static magnetic dipole-dipole interactions originate the interplay of the condensate at each site, are investigated. Classical-quantum correspondence in the large-spin limit is studied. Quantum chaotic features are studied through analysis of the irregular spectrum and time evolution of the Shannon entropy of wave packets. We show how the optical lattice strength influences the system dynamics, and is responsible for a transition from regular to irregular bahavior. PMID:18764032
Electronic conduction properties of indium tin oxide: single-particle and many-body transport.
Lin, Juhn-Jong; Li, Zhi-Qing
2014-08-27
Indium tin oxide (Sn-doped In2O3-δ or ITO) is a very interesting and technologically important transparent conducting oxide. This class of material has been extensively investigated for decades, with research efforts mostly focusing on the application aspects. The fundamental issues of the electronic conduction properties of ITO from room temperature down to liquid-helium temperatures have rarely been addressed thus far. Studies of the electrical-transport properties over a wide range of temperature are essential to unravelling the underlying electronic dynamics and microscopic electronic parameters. In this topical review, we show that one can learn rich physics in ITO material, including the semi-classical Boltzmann transport, the quantum-interference electron transport, as well as the many-body Coulomb electron-electron interaction effects in the presence of disorder and inhomogeneity (granularity). To fully reveal the numerous avenues and unique opportunities that the ITO material has provided for fundamental condensed matter physics research, we demonstrate a variety of charge transport properties in different forms of ITO structures, including homogeneous polycrystalline thin and thick films, homogeneous single-crystalline nanowires and inhomogeneous ultrathin films. In this manner, we not only address new physics phenomena that can arise in ITO but also illustrate the versatility of the stable ITO material forms for potential technological applications. We emphasize that, microscopically, the novel and rich electronic conduction properties of ITO originate from the inherited robust free-electron-like energy bandstructure and low-carrier concentration (as compared with that in typical metals) characteristics of this class of material. Furthermore, a low carrier concentration leads to slow electron-phonon relaxation, which in turn causes the experimentally observed (i) a small residual resistance ratio, (ii) a linear electron diffusion thermoelectric power in a wide temperature range 1-300 K and (iii) a weak electron dephasing rate. We focus our discussion on the metallic-like ITO material. PMID:25105780
The Hubbard dimer: a density functional case study of a many-body problem
NASA Astrophysics Data System (ADS)
Carrascal, D. J.; Ferrer, J.; Smith, J. C.; Burke, K.
2015-10-01
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green’s function, demonstrating the ‘failure’ of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.
The Hubbard dimer: a density functional case study of a many-body problem.
Carrascal, D J; Ferrer, J; Smith, J C; Burke, K
2015-10-01
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2. PMID:26380948
Danilov, Viatcheslav; Nagaitsev, Sergei; /Fermilab
2011-11-01
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.
Many-body effects in the spin-polarized electron transport through graphene nanoislands
Luo, Kaikai; Sheng, Weidong
2014-02-07
Spin-polarized electron transport through zigzag-edged graphene nanoislands is studied within the framework of the Pariser-Parr-Pople Hamiltonian. By including both short- and long-range electron-electron interactions, the electron conductance is calculated self-consistently for the hexagonal model on various substrates from which we are able to identify the effects of the many-body interactions in the electron transport. For the system in its lowest antiferromagnetic (AFM) state, the long-range interactions are shown to have negligible effect on the electron transport in the low-energy region in which the conductance is found quenched mainly by the short-range interactions. As the system is excited to its second AFM state, the short- and long-range interactions are found to have opposite effects on the electron transmission, i.e., the electron transmission is found to increase with either the suppression of the long-range interactions or the enhancement of the short-range interactions. When the system moves further into the ferromagnetic state, the conductance becomes spin dependent and its resonance is shown to exhibit a blue shift in an environment with stronger long-range interactions. The distinct impact of short- and long-range electron-electron interactions are attributed to their different effects on the spin polarization in the model system.
Potential of mean force between like-charged nanoparticles: Many-body effect.
Zhang, Xi; Zhang, Jin-Si; Shi, Ya-Zhou; Zhu, Xiao-Long; Tan, Zhi-Jie
2016-01-01
Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elusive many-body effect is attributed to ion-binding which is sensitive to ion concentration, ion valence, number of nanoparticles and charges on nanoparticles. PMID:26997415
Potential of mean force between like-charged nanoparticles: Many-body effect
Zhang, Xi; Zhang, Jin-Si; Shi, Ya-Zhou; Zhu, Xiao-Long; Tan, Zhi-Jie
2016-01-01
Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elusive many-body effect is attributed to ion-binding which is sensitive to ion concentration, ion valence, number of nanoparticles and charges on nanoparticles. PMID:26997415
Potential of mean force between like-charged nanoparticles: Many-body effect
NASA Astrophysics Data System (ADS)
Zhang, Xi; Zhang, Jin-Si; Shi, Ya-Zhou; Zhu, Xiao-Long; Tan, Zhi-Jie
2016-03-01
Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elusive many-body effect is attributed to ion-binding which is sensitive to ion concentration, ion valence, number of nanoparticles and charges on nanoparticles.
Electronic excitations: density-functional versus many-body Green's-function approaches
NASA Astrophysics Data System (ADS)
Onida, Giovanni; Reining, Lucia; Rubio, Angel
2002-04-01
Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy Σ and the electron-hole interaction. A good approximation for Σ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of Σ. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.
A many-body Hamiltonian for nanoparticles immersed in a polymer solution.
Woodward, Clifford E; Forsman, Jan
2015-01-13
We developed an analytical theory for the many-body potential of mean force (POMF) between N spheres immersed in a continuum chain fluid. The theory is almost exact for a Θ polymer solution in the protein limit (small particles, long polymers), where N-body effects are important. Polydispersity in polymer length according to a Schulz-Flory distribution emerges naturally from our analysis, as does the transition to the monodisperse limit. The analytical expression for the POMF allows for computer simulations employing the complete N-body potential (i.e., without n-body truncation; n < N). These are compared with simulations of an explicit particle/polymer mixture. We show that the theory produces fluid structure in excellent agreement with the explicit model simulations even when the system is strongly fluctuating, e.g., at or near the spinodal region. We also demonstrate that other commonly used theoretical approaches, such as truncation of the POMF at the pair level or the Asakura Oosawa model, are extremely inaccurate for these systems. PMID:25547161
Intervalley biexcitons and many-body effects in monolayer MoS2
NASA Astrophysics Data System (ADS)
Sie, Edbert J.; Frenzel, Alex J.; Lee, Yi-Hsien; Kong, Jing; Gedik, Nuh
2015-09-01
Interactions between two excitons can result in the formation of bound quasiparticles, known as biexcitons. Their properties are determined by the constituent excitons, with orbital and spin states resembling those of atoms. Monolayer transition metal dichalcogenides (TMDs) present a unique system where excitons acquire a new degree of freedom, the valley pseudospin, from which a novel intervalley biexciton can be created. These biexcitons comprise two excitons from different valleys, which are distinct from biexcitons in conventional semiconductors and have no direct analog in atomic and molecular systems. However, their valley properties are not accessible to traditional transport and optical measurements. Here, we report the observation of intervalley biexcitons in the monolayer TMD MoS2 using ultrafast pump-probe spectroscopy. By applying broadband probe pulses with different helicities, we identify two species of intervalley biexcitons with large binding energies of 60 and 40 meV. In addition, we also reveal effects beyond biexcitonic pairwise interactions in which the exciton energy redshifts at increasing exciton densities, indicating the presence of many-body interactions among them.
Applications of fidelity measures to complex quantum systems.
Wimberger, Sandro
2016-06-13
We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space. PMID:27140967
Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials
NASA Astrophysics Data System (ADS)
Throckmorton, Robert E.; Hofmann, Johannes; Barnes, Edwin; Das Sarma, S.
2015-09-01
We develop a theory for electron-electron interaction-induced many-body effects in three-dimensional Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine-structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies nonmonotonically as the low-energy, noninteracting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number (the multiplicity of electron species, e.g. ground-state valley degeneracy arising from the band structure) relative to the leading-order result. Thus, for materials with a larger multiplicity, the regime of velocity nonmonotonicity is reached for modest values of the coupling strength. This is in stark contrast to an approach based on a large-N expansion or the random phase approximation (RPA), where higher-order corrections are strongly suppressed for larger values of the Dirac cone multiplicity. This suggests that perturbation theory in the coupling constant (i.e., the loop expansion) and the RPA/large-N expansion are complementary in the sense that they are applicable in different parameter regimes of the theory. We show how our results for the ultraviolet renormalization of quasiparticle properties can be tested experimentally through measurements of quantities such as the optical conductivity or dielectric function (with carrier density or temperature acting as the scale being varied to induce the running coupling). Although experiments typically access the finite-density regime, we show that our zero-density results still capture clear many-body signatures that should be visible at higher temperatures even in real systems with disorder and finite doping.
Micheli, Fiorenza de; Zanelli, Jorge
2012-10-15
A degenerate dynamical system is characterized by a symplectic structure whose rank is not constant throughout phase space. Its phase space is divided into causally disconnected, nonoverlapping regions in each of which the rank of the symplectic matrix is constant, and there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems-in which the degeneracy cannot be eliminated by redefining variables in the action-the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.
Synthetic gauge fields and many-body physics in an optical lattice clock
NASA Astrophysics Data System (ADS)
Koller, Andrew P.; Wall, Michael L.; Li, Shuming; Zhang, Xibo; Cooper, Nigel R.; Ye, Jun; Rey, Ana Maria
2015-05-01
We propose the implementation of a synthetic gauge field in a 1D optical lattice clock and explore the resulting single-particle and many-body physics. The system can realize an effective two-leg ladder by using the two clock states as a synthetic dimension, together with the tunneling-coupled 1D lattice sites. A large flux per plaquette is naturally generated because the clock laser imprints a phase that varies significantly across lattice sites. We propose to use standard spectroscopic tools - Ramsey and Rabi spectroscopy - to probe the band structure and reveal signatures of the spin-orbit coupling, including chiral edge states and the modification of single-particle physics due to s-wave and p-wave interactions. These effects can be probed in spite of the relatively high temperatures (~ micro Kelvin) and weak interactions, thanks to the exquisite precision and sensitivity of the JILA Sr optical lattice clock. We also discuss the exciting possibility of using the nuclear spin degrees of freedom to realize more exotic synthetic dimension topologies and flux patterns. Supported by JILA-NSF-PFC-1125844, NSF-PIF- 1211914, ARO, AFOSR, AFOSR-MURI, and NDSEG.
Maximizing kinetic energy transfer in one-dimensional many-body collisions
NASA Astrophysics Data System (ADS)
Ricardo, Bernard; Lee, Paul
2015-03-01
The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions.
Hyperon-mixed neutron star with universal many-body repulsion
NASA Astrophysics Data System (ADS)
Yamamoto, Y.; Furumoto, T.; Yasutake, N.; Rijken, Th. A.
2016-02-01
Neutron stars with large masses ˜ 2M_{⊙} require the hard stiffness of equation of state (EoS) of neutron-star matter. On the other hand, hyperon mixing brings about remarkable softening of EoS. In order to solve this problem, a multi-pomeron exchange potential (MPP) is introduced as a model for the universal many-body repulsion in baryonic systems on the basis of the Extended Soft Core (ESC) baryon-baryon interaction. The strength of MPP is determined by analyzing the nucleus-nucleus scattering with the G -matrix folding model. The interactions in Λ N , Σ N and Ξ N channels are shown to be consistent with experimental indications. The EoS in neutron-star matter with hyperon mixing is obtained from ESC in addition of MPP, and mass-radius relations of neutron stars are derived. The maximum mass is shown to reach 2M_{⊙} even in the case of including hyperon mixing on the basis of model-parameters determined by terrestrial experiments.
GW Many-Body Perturbation Theory for Electron-Phonon Coupling Calculations
NASA Astrophysics Data System (ADS)
Faber, Carina
2015-03-01
Within many-body perturbation theory (MBPT) and the GW approximation, we study the electron-phonon coupling (EPC) in carbon-based systems, taking as paradigmatic examples the fullerene molecule, graphene and diamond. It has been demonstrated by several groups that the strength of the electron-phonon coupling potential is in these cases significantly underestimated at the DFT-LDA level, while GW calculations offer an excellent agreement with experiments. Similar results have been obtained for superconducting bismuthates and transition-metal chloronitrides. However, the related computational costs of evaluating the EPC strength at the GW level are high and thus represent strong limitations to a widespread application. We therefore discuss the accuracy of two less demanding alternatives on the MBPT level, namely the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further the constant screening approach. In the latter, variations of the screened Coulomb potential W upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We show that this latter approximation is most reliable, whereas the static COHSEX ansatz leads to substantial errors. These findings open the way for combining the present MBPT approach with efficient linear-response theories. C.F. gratefully acknowledges the Materials Theory Group, ETH Zurich for travel funding and the French CNRS and CEA for PhD funding. Computing time has been provided by the French GENCI-IDRIS supercomputing center under Contract No. i2012096655.
How many-body effects modify the van der Waals interaction between graphene sheets
NASA Astrophysics Data System (ADS)
Dobson, John; Gould, Tim; Vignale, Giovanni
2014-03-01
Cold undoped graphene sheets were previously predicted, via Random Phase approximation (RPA) arguments, to exhibit an unusual asymptotic van der Waals (vdW) interaction energy E = - KD-3 where D is the (large) separation between the two parallel graphene sheets. This is compared with D - 5 / 2 for 2D metals and D-4 for 2D insulators. Here we show that graphene is the first known system where effects beyond the RPA should make QUALITATIVE changes to the vdW force. For large separations, D > 10 nm where only πz-mediated vdW forces remain, we predict that the vdW interaction is substantially reduced from the RPA prediction, and has a different power law. This new D dependence is very sensitive to the form of the long-wavelength many-body renormalization of the velocity of the massless Dirac fermions, and may provide independent confirmation of the latter. We will briefly discuss issues involved in possible experiments. Work supported by the Australian Research Council, NSF and DIPC.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language. PMID:27088565
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
NASA Astrophysics Data System (ADS)
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
NASA Astrophysics Data System (ADS)
Schröder, Florian A. Y. N.; Chin, Alex W.
2016-02-01
We report the development of an efficient many-body algorithm for simulating open quantum system dynamics that utilizes a time-dependent variational principle for matrix product states to evolve large system-environment states. Capturing all system-environment correlations, we reproduce the nonperturbative, quantum-critical dynamics of the zero-temperature spin-boson model, and then exploit the many-body information to visualize the complete time-frequency spectrum of the environmental excitations. Our "environmental spectra" reveal correlated vibrational motion in polaronic modes which preserve their vibrational coherence during incoherent spin relaxation, demonstrating how environment information could yield valuable insights into complex quantum dissipative processes.
Explicit Local Integrals of Motion for the Many-Body Localized State
NASA Astrophysics Data System (ADS)
Rademaker, Louk; Ortuño, Miguel
2016-01-01
Recently, it has been suggested that the many-body localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert-space-preserving renormalization scheme that iteratively finds such integrals of motion exactly. Our method is based on the consecutive action of a similarity transformation using displacement operators. We show, as a proof of principle, localization and the delocalization transition in interacting fermion chains with random on-site potentials. Our scheme of consecutive displacement transformations can be used to study many-body localization in any dimension, as well as disorder-free Hamiltonians.
Stability of Local Quantum Dissipative Systems
NASA Astrophysics Data System (ADS)
Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David
2015-08-01
Open quantum systems weakly coupled to the environment are modeled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Lindbladians. In the setting of quantum many-body systems on a lattice it is natural to consider Lindbladians that decompose into a sum of local interactions with decreasing strength with respect to the size of their support. For both practical and theoretical reasons, it is crucial to estimate the impact that perturbations in the generating Lindbladian, arising as noise or errors, can have on the evolution. These local perturbations are potentially unbounded, but constrained to respect the underlying lattice structure. We show that even for polynomially decaying errors in the Lindbladian, local observables and correlation functions are stable if the unperturbed Lindbladian has a unique fixed point and a mixing time that scales logarithmically with the system size. The proof relies on Lieb-Robinson bounds, which describe a finite group velocity for propagation of information in local systems. As a main example, we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates, which may not preserve detailed balance.
Curtright, Thomas; Mezincescu, Luca
2007-09-15
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+{nu}){sup 2}+{sigma}{sub k>0}{mu}{sub k} exp(ikx). In some nontrivial cases, equivalent Hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.
Dynamical and statistical modelling of many body collisions Part II: Energy exchange
NASA Astrophysics Data System (ADS)
Agbormbai, A. A.
2001-08-01
While rarefied gas dynamics has traditionally assumed a dilute gas, whose densities are so low that only binary collisions and single-body gas surface interactions occur, expressions for many-body collision rates and for many-body gas surface interaction (GSI) rates seem to suggest that at lower heights the dilute gas is not valid. In particular, in the pure rarefied regime, two-body GSIs and some three-body interactions occur whereas, in the transition regime into continuum flow, four body collisions and four-body GSIs occur. In this paper I formulate the problem of many-body energy exchange as a complement to the problem of many body scattering which I formulated in Part I. I showed there that a many body collision can be formulated in terms of the motion of a number of reduced particles which scatter in space as well as exchange energy with one another and with the center of mass. In this paper I concentrate on the energy exchange and present a statistical theory based on reciprocity or detailed balance. I derive statistical transformation models for three and four body encounters. The same techniques can be applied to any number of interacting bodies—the final transformation model simply becomes more complex. The determination of the post-collision energies of the reduced particles makes it possible to calculate their post-collision speeds. This is needed, in combination with the scattering results, to calculate the laboratory velocities of the interacting particles. The approach produces results for use in the Direct Simulation Monte Carlo (DSMC) method, which is the standard method of computing rarefied gas phenomena.
Charge optimized many-body (COMB) potential for dynamical simulation of Ni–Al phases
NASA Astrophysics Data System (ADS)
Kumar, Aakash; Chernatynskiy, Aleksandr; Liang, Tao; Choudhary, Kamal; Noordhoek, Mark J.; Cheng, Yu-Ting; Phillpot, Simon R.; Sinnott, Susan B.
2015-08-01
An interatomic potential for the Ni–Al system is presented within the third-generation charge optimized many-body (COMB3) formalism. The potential has been optimized for Ni3Al, or the γ‧ phase in Ni-based superalloys. The formation energies predicted for other Ni–Al phases are in reasonable agreement with first-principles results. The potential further predicts good mechanical properties for Ni3Al, which includes the values of the complex stacking fault (CSF) and the anti-phase boundary (APB) energies for the (1 1 1) and (1 0 0) planes. It is also used to investigate dislocation propagation across the Ni3Al (1 1 0)–Ni (1 1 0) interface, and the results are consistent with simulation results reported in the literature. The potential is further used in combination with a recent COMB3 potential for Al2O3 to investigate the Ni3Al (1 1 1)–Al2O3 (0 0 01) interface, which has not been modeled previously at the classical atomistic level due to the lack of a reactive potential to describe both Ni3Al and Al2O3 as well as interactions between them. The calculated work of adhesion for this interface is predicted to be 1.85 J m‑2, which is in agreement with available experimental data. The predicted interlayer distance is further consistent with the available first-principles results for Ni (1 1 1)–Al2O3 (0 0 0 1).
Energy Gaps and Interaction Blockade in Confined Quantum Systems
Capelle, K.; Borgh, M.; Kaerkkaeinen, K.; Reimann, S. M.
2007-07-06
We investigate universal properties of strongly confined particles that turn out to be dramatically different from what is observed for electrons in atoms and molecules. For a large class of harmonically confined systems, such as small quantum dots and optically trapped atoms, many-body particle addition and removal energies, and energy gaps, are accurately obtained from single-particle eigenvalues. Transport blockade phenomena are related to the derivative discontinuity of the exchange-correlation functional. This implies that they occur very generally, with Coulomb blockade being a particular realization of a more general phenomenon. In particular, we predict a van der Waals blockade in cold atom gases in traps.
Hybrid Quantum Systems with Circuit Quantum Electrodynamics
NASA Astrophysics Data System (ADS)
Schuster, David
2012-02-01
Quantum Information Processing presents daunting challenges, with competing requirements of fast manipulation, long storage, and long distance transport of fragile quantum states. In aggregate, many of the challenges quantum computation have been met with nanosecond manipulations (quantum circuits), coherence times measured in seconds (atomic ions/nuclear spins), and entanglement transported over kilometers (linear optics), yet thus far no system has achieved all of the necessary components simultaneously. One promising direction is to leverage the best aspects of each system in a hybrid system, much as is done in a conventional computer, where transistors provide fast processing, magnetic memory provides massive long term storage, and information is transmitted via microwaves or fiber optics. A review of the constituent quantum systems, and the types of couplings between them will be presented. The coupling of a superconducting cavity/qubit system to electrons floating on helium will be discussed as an example of how to construct a hybrid system. Recent results on trapping and detection of electrons on helium using a superconducting cavity will be presented.
Effective potential for many-body interactions in some properties of the HFD-like solids
NASA Astrophysics Data System (ADS)
Abbaspour, Mohsen; Farmanbar, Alireza; Borzouie, Zahra
2015-12-01
We have determined the room-temperature equation of state for the HFD-like solids (such as Ar, Kr, Xe, CH4, CO2, N2, and O2) using the two-body HFD-like potentials from molecular dynamics simulation at high pressures. A simple and accurate empirical many-body expression has also been used with the two-body potential for the HFD-like solids without requiring an expensive three-body calculation. The configurational energy and the exact equation of state using the new model have been obtained in good agreement with the experiment. Our predicted results of the elastic constants also indicated that our new effective (many-body corrected) potential improves the two-body values of solids Ar, Kr, and CO2 to get better agreement with the experiment.
Many-body interaction effects on the low-k structure of liquid Kr
NASA Astrophysics Data System (ADS)
Guarini, E.; Magli, R.; Tau, M.; Barocchi, F.; Casanova, G.; Reatto, L.
2001-05-01
Neutron diffraction measurements and theoretical calculations of the structure factor S(k) of liquid Kr are extended to small k values (k<4 nm-1). The results show that many-body interaction contributions have an increasing effect on S(k) as k-->0, reaching at least 40% of the measured intensity. Both the phase diagram and the low-k structural data of dense Kr turn out to be closely reproduced by the hierarchical reference theory if additional many-body forces are taken into account by an augmented strength of the Axilrod-Teller triple-dipole potential. The experimental density derivative of S(k) is also used for a very sensitive test of the theories and interaction models considered here.
Cosmological constraints to dark matter with two- and many-body decays
NASA Astrophysics Data System (ADS)
Blackadder, Gordon; Koushiappas, Savvas M.
2016-01-01
We present a study of cosmological implications of generic dark matter decays. We consider two-body and many-body decaying scenarios. In the two-body case the massive particle has a possibly relativistic kick velocity and thus possesses a dynamical equation of state. This has implications to the expansion history of the Universe. We use recent observational data from the cosmic microwave background, baryon acoustic oscillations and supernovae type Ia to obtain constraints on the lifetime of the dark matter particle. We find that for an energy splitting where more than 40% of the dark matter particle energy is transferred to massless, relativistic particles in the two-body case, or more than 50% in the many-body case, lifetimes less than the age of the Universe are excluded at more than 95% confidence. When the energy splitting falls to 10% the lifetime is constrained to be more than roughly half the age.
Hierarchy of multiple many-body interaction scales in high-temperature superconductors
Hussain, Zahid; Meevasana, W.; Zhou, X.J.; Sahrakorpi, S.; Lee, W.S.; Yang, W.L.; Tanaka, K.; Mannella, N.; Yoshida, T.; Lu, D.H.; Chen, Y.L.; He, R.H.; Lin, Hsin; Komiya, S.; Ando, Y.; Zhou, F.; Ti, W.X.; Xiong, J.W.; Zhao, Z.X.; Sasagawa, T.; Kakeshita, T.; Fujita, K.; Uchida, S.; Eisaki, H.; Fujimori, A.; Hussain, Z.; Markiewicz, R.S.; Bansil, A.; Nagaosa, N.; Zaanen, J.; Devereaux, T.P.; Shen, Z.X.
2006-12-21
To date, angle-resolved photoemission spectroscopy has been successful in identifying energy scales of the many-body interactions in correlated materials, focused on binding energies of up to a few hundred meV below the Fermi energy. Here, at higher energy scale, we present improved experimental data from four families of high-T{sub c} superconductors over a wide doping range that reveal a hierarchy of many-body interaction scales focused on: the low energy anomaly ('kink') of 0.03-0.09eV, a high energy anomaly of 0.3-0.5eV, and an anomalous enhancement of the width of the LDA-based CuO{sub 2} band extending to energies of {approx} 2 eV. Besides their universal behavior over the families, we find that all of these three dispersion anomalies also show clear doping dependence over the doping range presented.
Evolving nuclear many-body forces with the similarity renormalization group
Jurgenson, E. D.; Navratil, P.; Furnstahl, R. J.
2011-03-15
In recent years, the Similarity Renormalization Group has provided a powerful and versatile means to soften interactions for ab initio nuclear calculations. The substantial contribution of both induced and initial three-body forces to the nuclear interaction has required the consistent evolution of free-space Hamiltonians in the three-particle space. We present the most recent progress on this work, extending the calculational capability to the p-shell nuclei and showing that the hierarchy of induced many-body forces is consistent with previous estimates. Calculations over a range of the flow parameter for {sup 6}Li, including fully evolved NN + 3N interactions, show moderate contributions due to induced four-body forces and display the same improved convergence properties as in lighter nuclei. A systematic analysis provides further evidence that the hierarchy of many-body forces is preserved.
The hierarchy of multiple many-body interaction scales in high-temperature superconductors
Meevasana, W.
2010-05-03
To date, angle-resolved photoemission spectroscopy has been successful in identifying energy scales of the many-body interactions in correlated materials, focused on binding energies of up to a few hundred meV below the Fermi energy. Here, at higher energy scale, we present improved experimental data from four families of high-T{sub c} superconductors over a wide doping range that reveal a hierarchy of many-body interaction scales focused on: the low energy anomaly ('kink') of 0.03-0.09eV, a high energy anomaly of 0.3-0.5eV, and an anomalous enhancement of the width of the LDA-based CuO{sub 2} band extending to energies of {approx} 2 eV. Besides their universal behavior over the families, we find that all of these three dispersion anomalies also show clear doping dependence over the doping range presented.
Inadequacy of the statistical many-body model for molecular infrared absorption in the far wings
NASA Technical Reports Server (NTRS)
Fowler, B. W.; Sung, C. C.
1976-01-01
It is known that the infrared absorption coefficient of CO2 in the far wings is far less than what is derived from the assumption of a Lorentzian absorption profile. Sorgen and Ben-Aryeh (1972) tried to show that by incorporating the statistical many-body model into impact theory, the discrepancy between the Lorentzian absorption profile and the experimental infrared absorption coefficient can be removed. This paper attempts to show that the high frequency or short-time property of the dipole-dipole interaction cannot be adequately explained by the many-body model; in other words, the statistical model as conventionally understood is not applicable to infrared spectral lines in the far wings.
Many-body localization transition in Rokhsar-Kivelson-type wave functions
NASA Astrophysics Data System (ADS)
Chen, Xiao; Yu, Xiongjie; Cho, Gil Young; Clark, Bryan K.; Fradkin, Eduardo
2015-12-01
We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the random energy model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with the subsystem size: scaling with the entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a subextensive scaling between these limits. Near the phase transition point, the fluctuations of the Rényi entropies are non-Gaussian. We find that Rényi entropies with different Rényi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior.
Combining DFT and Many-body Methods to Understand Correlated Materials
NASA Astrophysics Data System (ADS)
Solovyev, Igor
2007-03-01
Electronic and magnetic properties of strongly-correlated systems are typically controlled by a limited number of electronic states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the first-principles methods of electronic structure calculations, based on the density-functional theory (DFT), with model many- body methods, formulated in a restricted Hilbert space of states near the Fermi level. The core of this project is the construction of ``ab initio model Hamiltonians'', which would incorporate the physics of on-site Coulomb correlations and provide a transparent physical picture for the low-energy properties of strongly- correlated systems. First, I will describe a systematic procedure for constructing such an effective Hubbard-type model, which consists of three major steps, starting from the electronic structure in the local- density approximation.^1 (i) Construction of the kinetic-energy part using an exact version of the downfolding method;^1,2 (ii) Construction of the Wannier functions; (iii) Calculation of screened Coulomb interactions using a hybrid approach, which combines the random phase approximation with the constraint DFT.^1,3 Then, I will illustrate abilities of this method for resolving a number of controversial issues, related with the interplay of the experimental lattice distortion and magnetic properties of four narrow t2g band perovskite oxides (YTiO3, LaTiO3, YVO3, and LaVO3), for which the obtained Hamiltonian was solved using a number of techniques, including the Hartree-Fock (HF) approximation,^4 the second-order perturbation theory and the t-matrix approach for the correlation energy,^ 4,5 and a variational superexchange theory, which takes into account the multiplet structure of the atomic states.^4 I will argue that the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favors the formation of experimental magnetic structures in YTiO3, YVO3, and LaVO3, even at the level of HF approximation. The correlation effects systematically improve the agreement with the experimental data and additionally stabilize the experimentally observed G- and C-type antiferromagnetic states in YVO3 and LaVO3. The role of relativistic spin-orbit interaction will be also discussed. ^1 I. V. Solovyev, Phys. Rev. B 73, 155117 (2006). ^2 I. V. Solovyev, Z. V. Pchelkina, and V. I. Anisimov, cond- mat/0608528. ^3 I. V. Solovyev and M. Imada, Phys. Rev. B 71, 045103 (2005). ^4 I. V. Solovyev, Phys. Rev. B 74, 054412 (2006). ^5 I. V. Solovyev, cond-mat/0608625.
Non-local propagation of correlations in quantum systems with long-range interactions.
Richerme, Philip; Gong, Zhe-Xuan; Lee, Aaron; Senko, Crystal; Smith, Jacob; Foss-Feig, Michael; Michalakis, Spyridon; Gorshkov, Alexey V; Monroe, Christopher
2014-07-10
The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective 'light cone'. However, little is known about the propagation speed in systems with long-range interactions, because analytic solutions rarely exist and because the best long-range bound is too loose to accurately describe the relevant dynamical timescales for any known spin model. Here we apply a variable-range Ising spin chain Hamiltonian and a variable-range XY spin chain Hamiltonian to a far-from-equilibrium quantum many-body system and observe its time evolution. For several different interaction ranges, we determine the spatial and time-dependent correlations, extract the shape of the light cone and measure the velocity with which correlations propagate through the system. This work opens the possibility for studying a wide range of many-body dynamics in quantum systems that are otherwise intractable. PMID:25008525
NASA Astrophysics Data System (ADS)
Jiang, Dansha
The relativistic many-body perturbation theory (MBPT) calculations for matrix elements of divalent atoms and ions is extended to third-order. The one-particle and two-particle contributions are carefully examined and a complete angular reduction of the third-order amplitudes is carried out. Example calculations are performed on beryllium and magnesium isoelectronic sequences. Oscillator strengths, transition probabilities, and lifetimes are calculated for selected ions. Significant improvement in comparison with second-order MBPT results is observed. The relativistic all-order method is introduced for high-precision calculations of atomic properties in monovalent systems, where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory. Energies, reduced electric-dipole matrix elements and lifetimes are calculated and compared with available experiments for the low-lying excited np and nd states in Sr+, Ba+ and Ra+ atoms. Electric-quadrupole moments of the metastable nd3/2 and nd 5/2 states of Ca+, Sr+, and Ba+ are evaluated for the optical clock development applications. Third-order MBPT is used to evaluate the contributions from high partial waves and Breit interaction, and a semi-empirical scaling procedure is carried out to evaluate the remaining omitted correlation corrections. An extensive study of the uncertainties establishes the accuracy of our recommended values as 0.5 - 1% depending on the particular ion. Extra attention is paid to the 5 s-4d5/2 clock transition in 88 Sr+. The scalar polarizabilities of the 5s and 4d5/2 states and the tensor polarizability of the 4d5/2 state are calculated through the summation of individual possible dipole transition contributions. A complete analysis on the uncertainties of the static polarizabilities. The black-body radiation (BBR) shift is evaluated to be 0.250(9) Hz at room temperature, T = 300 K. The dynamic correction to the electric-dipole contribution and the multipolar corrections due to M1 and E2 transitions were estimated and found to be small at the present level of accuracy. CI + all-order method is used for the calculations of the atomic properties in the divalent systems. This method combines the all-order approach currently used in precision calculations of monovalent system with the configuration-interaction (CI) approach that is applicable for many-electron systems. Energies are calculated in different orders of approximations for several low-lying excited states in the divalent systems from Mg to Hg. The results are compared with experiments. The static and frequency-dependent polarizabilities are evaluated for the lowest nsns 1S0 and nsnp 3P0 states in Sr, Zn, Cd, and Hg atoms. Magic wavelengths are found for the 1 S0 -3 P 0 transitions in those systems by matching the ac Stark shifts of the upper and lower states. The preliminary magic wavelength for the Sr system is in 0.03% agreement with the recent high-precision experiment performed by Brusch et al. [PRL, 96, 103003(2006)]. Other preliminary calculations are performed for the electric-dipole transition matrix elements in Sr, Zn, Cd, and Hg atoms. Transition rates of the ns 2 1S0-nsnp 1P1 resonant line and the ns 2 1S0-nsnp 3P1 intercombination line are evaluated for these systems. Major contributions to the scattering rates are evaluated for the cases where atoms are trapped at their magic wavelengths with a shallow potential depth.
Quantum dephasing of a two-state system by a nonequilibrium harmonic oscillator
Martens, Craig C.
2013-07-14
In this paper, we investigate coherent quantum dynamics in a nonequilibrium environment. We focus on a two-state quantum system strongly coupled to a single classical environmental oscillator, and explore the effect of nonstationary statistical properties of the oscillator on the quantum evolution. A simple nonequilibrium model, consisting of an oscillator with a well-defined initial phase which undergoes subsequent diffusion, is introduced and studied. Approximate but accurate analytic expressions for the evolution of the off-diagonal density matrix element of the quantum system are derived in the second-order cumulant approximation. The effect of the initial phase choice on the subsequent quantum evolution is quantified. It is observed that the initial phase can have a significant effect on the preservation of coherence on short time scales, suggesting this variable as a control parameter for optimizing coherence in many-body quantum systems.
Relaxation Dynamics and Pre-thermalization in an isolated Quantum System
NASA Astrophysics Data System (ADS)
Schmiedmayer, Jörg
2012-02-01
Understanding non-equilibrium dynamics of many-body quantum systems is crucial for understanding many fundamental and applied physics problems ranging from decoherence and equilibration to the development of future quantum technologies such as quantum computers which are inherently non-equilibrium quantum systems. One of the biggest challenges is that there is no general approach to characterize the resulting quantum states. In this talk I will present how to use the full distribution functions of a quantum observable to study the relaxation dynamics in one-dimensional quantum systems and to characterize the underlying many body states. Interfering two 1 dimensional quantum gases allows to study how the coherence created between the two many body systems by the splitting process [1] slowly dies by coupling to the many internal degrees of freedom available [2]. To reveal the nature of the quantum states behind this de-coherence we analyze the interference of the two evolving quantum systems. The full distribution function of the shot to shot variations of the interference patterns [3,4], especially its higher moments, allows characterizing the underlying physical processes [5]. Two distinct regimes are clearly visible in the experiment: for short length scales the system is characterized by spin diffusion, for long length scales by spin decay [6]. After a rapid evolution the distributions approach a steady state which can be characterized by thermal distribution functions. Interestingly, its (effective) temperature is over five times lower than the kinetic temperature of the initial system. Our system, being a weakly-interacting Bosons in one dimension, is nearly integrable and the dynamics is constrained by constants of motion which leads to the establishment of a generalized Gibbs ensemble and pre-thermalization. We therefore interpret our observations as an illustration of the fast relaxation of a nearly integrable many-body system to a quasi-steady state through de-phasing. The observation of an effective temperature significant different from the expected kinetic temperature supports the observation of the generalized Gibbs state [6]. [4pt] [1] T. Schumm et al. Nature Physics, 1, 57 (2005).[0pt] [2] S. Hofferberth et al. Nature 449, 324 (2007).[0pt] [3] A. Polkovnikov, et al. Proc. Natl. Acad. Sci. 103, 6125 (2006); V. Gritsev, et al., Nature Phys. 2, 705 (2006); [0pt] [4] S. Hofferberth et al. Nature Physics 4, 489 (2008); [0pt] [5] T. Kitagawa, et al., Phys. Rev. Lett. 104, 255302 (2010); New Journal of Physcs, 13 073018 (2011)[0pt] [6] Gring et al., to be published
Ab initio many-body treatment of the electronic structure of metals
NASA Astrophysics Data System (ADS)
Peschel, O.; Schnell, I.; Czycholl, G.
2005-10-01
We propose and apply a combination of an ab initio (band-structure) calculation with a many-body treatment including screening effects. We start from a linearized muffin-tin orbital (LMTO) calculation to determine the Bloch functions for the Hartree one-particle Hamiltonian, from which we calculate the static susceptibility and dielectric function within the standard random phase approximation (RPA). From the Bloch functions we obtain maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and unscreened and screened Coulomb matrix elements are calculated. This yields a multi-band Hamiltonian in second quantization with ab initio parameters, for which screening has been taken into account within the simplest standard approximation. Then, established methods of many-body theory are used. We apply this concept to a simple metal, namely lithium (Li). Here the maximally localized Wannier functions turn out to be of the sp3-orbital kind. Furthermore, only the on-site contributions of the screened Coulomb matrix elements are relevant, and a generalized, four-band Hubbard model is justified. The screened on-site Coulomb matrix elements are considerably smaller than the band width because of which it is sufficient to calculate the selfenergy in weak-coupling approximation. We compare results obtained within the screened Hartree-Fock approximation (HFA) and within the second-order perturbation theory (SOPT) in the Coulomb matrix elements for Li and find that many-body effects are small but not negligible even for this simple metal.
Quantum study of the H3 system
NASA Astrophysics Data System (ADS)
Peng, Zhengwei
In this thesis, an ab initio quantum; study of both electronic and nuclear motions of the H3 system is presented. Results of the ab initio calculations for the lowest four electronic potential energy surfaces of the H3 system are given, as well as for the electric dipole transition moments between them. The calculated Rydberg spectra compare well with previous calculations and with known experimental results. The ground state and the third excited state surfaces have been fitted using the rotated Morse cubic spline (RMCS) method. The ro-vibrational eigenstates of H3 on the upper sheet of the Double Many Body Expansion (DMBE) surface were calculated using a variational method and a new hyperspherical coordinate propagation method. The full P3 nuclear permutation symmetry and the molecular Aharonov-Bohm (MAB) (or geometric phase) effect were included in the hyperspherical coordinate propagation method. The MAB effect has a profound influence on the bound ro-vibrational states of the H3 system. The ro-vibrational bound states of H3 in the third excited 2pz 2A"2 electronic state were also studied. The Rydberg nature of this electronic state leads to ro-vibrational nuclear motion similar to that of the H+3 ion. The comparison between the calculated values of the ro-vibrational constants and the corresponding experimental results suggests that the 2pz 2A"2 RMCS surface still needs some improvement.
Communication: Dominance of extreme statistics in a prototype many-body Brownian ratchet
Hohlfeld, Evan; Geissler, Phillip L.
2014-10-28
Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in filaments' spatial distribution.
Two novel classes of solvable many-body problems of goldfish type with constraints
NASA Astrophysics Data System (ADS)
Calogero, F.; Gómez-Ullate, D.
2007-05-01
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
Molecular dynamics simulation of interparticle spacing and many-body effect in gold supracrystals.
Liu, X P; Ni, Y; He, L H
2016-04-01
Interparticle spacing in supracrystals is a crucial parameter for photoelectric applications as it dominates the transport rates between neighboring nanoparticles (NPs). Based on large-scale molecular dynamics simulations, we calculate interparticle spacing in alkylthiol-stabilized gold supracrystals as a function of the NP size, ligand length and external pressure. The repulsive many-body interactions in the supracrystals are also quantified by comparing the interparticle spacing with that between two individual NPs at equilibrium. Our results are consistent with available experiments, and are expected to help precise control of interparticle spacing in supracrystal devices. PMID:26909856
Many-body electronic structure calculations of Eu-doped ZnO
NASA Astrophysics Data System (ADS)
Lorke, M.; Frauenheim, T.; da Rosa, A. L.
2016-03-01
The formation energies and electronic structure of europium-doped zinc oxide has been determined using DFT and many-body G W methods. In the absence of intrisic defects, we find that the europium-f states are located in the ZnO band gap with europium possessing a formal charge of 2+. On the other hand, the presence of intrinsic defects in ZnO allows intraband f -f transitions otherwise forbidden in atomic europium. This result corroborates with recently observed photoluminescence in the visible red region S. Geburt et al. [Nano Lett. 14, 4523 (2014), 10.1021/nl5015553].
On the atomic roughness of solid-vapor interfaces - Significance of many-body interactions
NASA Technical Reports Server (NTRS)
Chen, Jenn-Shing; Ming, Nai-Ben; Rosenberger, Franz
1986-01-01
Published experimental data on the atomic roughness of solid-vapor interfaces (SVIs) are compiled in a table and compared with the predictions of theoretical models based on the Bragg-Williams approximation (e.g., Jackson, 1958). Significant discrepancies are observed, and a new model employing site-dependent bond strengths based on many-body-interaction effects is developed and demonstrated. Predictions for Cu, Pb, and Zn are presented in extensive tables and graphs and characterized in detail: good agreement with experimental observations of anisotropic melting is obtained.
Benacquista, M.J.
1988-01-01
The gravitational many-body parameterized post-Newtonian (PNN) Lagrangian for compact celestial bodies is extended to second post-Newtonian order and is constrained to exhibit the invariances observed in nature-generalized Lorentz invariance, the strong equivalence principle, and the isotropy of the gravitational potential. These invariances are imposed on the Lagrangian using an empirical approach which is based on calculated observables rather than through formal procedures involving post-Newtonian approximations of transformations. When restricted in this way, the Lagrangian possesses two free parameters which can be related to light-deflection experiments and the effect of an environment of proximate matter on such experiments.
NASA Astrophysics Data System (ADS)
Fan, Zheyong; Pereira, Luiz Felipe C.; Wang, Hui-Qiong; Zheng, Jin-Cheng; Donadio, Davide; Harju, Ari
2015-09-01
We derive expressions of interatomic force and heat current for many-body potentials such as the Tersoff, the Brenner, and the Stillinger-Weber potential used extensively in molecular dynamics simulations of covalently bonded materials. Although these potentials have a many-body nature, a pairwise force expression that follows Newton's third law can be found without referring to any partition of the potential. Based on this force formula, a stress applicable for periodic systems can be unambiguously defined. The force formula can then be used to derive the heat current formulas using a natural potential partitioning. Our heat current formulation is found to be equivalent to most of the seemingly different heat current formulas used in the literature, but to deviate from the stress-based formula derived from two-body potential. We validate our formulation numerically on various systems described by the Tersoff potential, namely three-dimensional silicon and diamond, two-dimensional graphene, and quasi-one-dimensional carbon nanotube. The effects of cell size and production time used in the simulation are examined.
Topology, localization, and quantum information in atomic, molecular and optical systems
NASA Astrophysics Data System (ADS)
Yao, Norman Ying
The scientific interface between atomic, molecular and optical (AMO) physics, condensed matter, and quantum information science has recently led to the development of new insights and tools that bridge the gap between macroscopic quantum behavior and detailed microscopic intuition. While the dialogue between these fields has sharpened our understanding of quantum theory, it has also raised a bevy of new questions regarding the out-of-equilibrium dynamics and control of many-body systems. This thesis is motivated by experimental advances that make it possible to produce and probe isolated, strongly interacting ensembles of disordered particles, as found in systems ranging from trapped ions and Rydberg atoms to ultracold polar molecules and spin defects in the solid state. The presence of strong interactions in these systems underlies their potential for exploring correlated many-body physics and this thesis presents recent results on realizing fractionalization and localization. From a complementary perspective, the controlled manipulation of individual quanta can also enable the bottom-up construction of quantum devices. To this end, this thesis also describes blueprints for a room-temperature quantum computer, quantum credit cards and nanoscale quantum thermometry.
Many-body effects in doped graphene on a piezoelectric substrate
NASA Astrophysics Data System (ADS)
Sols, F.; Gonzalez, D. G.; Zapata, I.; Schiefele, J.; Guinea, F.
We study theoretically the role of piezoelectric acoustic phonons in the context of piezoelectric substrates covered by graphene. They are responsible for effective, substrate dependent electron-electron interactions which can be strong and give rise to novel many-body effects. We present a new derivation of the electron-phonon interaction matrix element which generalizes previous calculations made within the simpler and not always justified isotropic approximation. We study several many-body effects, including the temperature-dependent phonon renormalization due to the electron cloud surrounding the lattice vibration, as well as the electron self-energies arising from the effective electron-electron interactions in the perturbative G0 W approximation. We also perform calculations of the graphene electron mobility on substrates with various levels of piezoelectricity. Finally, we discuss how these piezoelectric phonons can influence the superconducting instability. For completeness, we compare our results with the situation found for the two-dimensional electron gas and for conventional three-dimensional BCS superconductors. Work supported by MINECO (Spain), CEI Moncloa UCM-UPM, ERC (EU), and the European Commission Graphene Flagship.
Scale-adaptive tensor algebra for local many-body methods of electronic structure theory
Liakh, Dmitry I
2014-01-01
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).
Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
NASA Astrophysics Data System (ADS)
Chen, Xiao; Yu, Xiongjie; Cho, Gil Young; Clark, Bryan; Fradkin, Eduardo
We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the Renyi entropies are non-Gaussian. We find that Renyi entropies with different Renyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior. This work was supported in part by DMR-1064319 and DMR-1408713 (XC,GYC,EF) at the University of Illinois, PHY11-25915 at KITP (EF), DOE, SciDAC FG02-12ER46875 (BKC and XY), and the Brain Korea 21 PLUS Project of Korea Government (GYC).
Quantifying many-body effects by high-resolution Fourier transform scanning tunneling spectroscopy
NASA Astrophysics Data System (ADS)
Grothe, Stephanie; Johnston, Steve; Chi, Shun; Dosanjh, Pinder; Burke, Sarah A.; Pennec, Yan
2014-03-01
The properties of solids are influenced by many-body effects that arise from the interactions of the electrons with each other and with the multitude of collective lattice, spin or charge excitations. We apply the technique of Fourier transform scanning tunneling spectroscopy (FT-STS) to probe the many-body effects of the Ag(111) surface state. A renormalization of the otherwise parabolic dispersion induced by electron-phonon interactions is revealed that has not previously been resolved by any technique, allowing us to extract the real part of the self-energy. Furthermore, we show how variations in the intensity of the FT-STS signal are related to the imaginary part of the self-energy. We accurately modeled the experimental data with the T-matrix formalism for scattering from a single impurity, assuming that the surface electrons are dressed by electron-electron and electron-phonon interactions. A Debye energy of ℏΩD = 14 +/- 1 meV and an electron-phonon coupling strength of λ = 0 . 13 +/- 0 . 02 was extracted. Our results advance FT-STS as a tool to simultaneously extract real and imaginary parts of the self-energy for both occupied and unoccupied states with a momentum and energy resolution competitive with angle-resolved photoemission spectroscopy.
Establishing conservation laws in pair-correlated many-body theories: T-matrix approaches
NASA Astrophysics Data System (ADS)
He, Yan; Levin, K.
2014-01-01
We address conservation laws associated with current, momentum, and energy and show how they can be satisfied within many body theories which focus on pair correlations. Of interest are two well known T-matrix theories which represent many body theories which incorporate pairing in the normal state. The first of these is associated with the Nozieres Schmitt-Rink theory, while the second involves the T matrix of a BCS-Leggett-like state as identified by Kadanoff and Martin. T-matrix theories begin with an ansatz for the single particle self energy and are to be distinguished from Φ-derivable theories which introduce an ansatz for a particular contribution to the thermodynamical potential. Conservation laws are equivalent to Ward identities which we address in some detail here. Although Φ-derivable theories are often referred to as "conserving theories," a consequence of this work is the demonstration that these two T-matrix approaches similarly can be made to obey all conservation laws. When simplifying approximations are made in Φ-derivable or other theories, one has to take care that the end results are not incompatible with conservation.
NASA Astrophysics Data System (ADS)
Bhattacharyya, Satadal; Chakrabarti, Barnali
2016-02-01
We present a correlated many-body approach to calculate the distribution function and fluctuations for a Bose-Einstein condensate with N interacting atoms in the harmonic confinement. The present formulation uses the recursion relation for the canonical ensemble partition function (Z ) . Z is calculated from the energy spectrum of the many-body effective potential, which keeps all possible two-body correlations and uses the realistic interatomic interaction. The condensate statistics are in very good agreement with earlier results of an ideal gas for which exact statistical moments for all temperature are known. We also present the numerical results of condensate statistics for real experimental situations. The calculated moments nicely exhibit the mesoscopic effect for a few hundred atoms, whereas the sharp fall in the variance for the large condensate near the critical temperature shows the possibility of phase transition. We also calculate the critical temperature for the mesoscopic regime. Our present calculation mimics the JILA experiment with 87Rb atoms.
Experimental observation of spin-dependent electron many-body effects in CdTe
Horodyská, P.; Němec, P. Novotný, T.; Trojánek, F.; Malý, P.
2014-08-07
In semiconductors, the spin degree of freedom is usually disregarded in the theoretical treatment of electron many-body effects such as band-gap renormalization and screening of the Coulomb enhancement factor. Nevertheless, as was observed experimentally in GaAs, not only the single-particle phase-space filling but also many-body effects are spin sensitive. In this paper, we report on time- and polarization-resolved differential transmission pump-probe measurements in CdTe, which has the same zincblende crystal structure but different material parameters compared to that of GaAs. We show experimentally that at room temperature in CdTe—unlike in GaAs—the pump-induced decrease of transmission due to the band-gap renormalization can even exceed the transmission increase due to the phase-space filling, which enables to measure directly the spin-sensitivity of the band-gap renormalization. We also observed that the influence of the band-gap renormalization is more prominent at low temperatures.
Ab initio calculations of many-body interactions for compressed solid argon.
Tian, Chunling; Liu, Fusheng; Cai, Lingcang; Yuan, Hongkuan; Chen, Hong; Zhong, Mingmin
2015-11-01
An investigation on many-body effects of solid argon at high pressure was conducted based on a many-body expansion of interaction energy. The three- and four-body terms in the expansion were calculated using the coupled-cluster method with single, double, and noniterative triple theory and incremental method, in which the configurations of argon trimers and tetramers were chosen as the same as those in the actual lattice. The four-body interactions in compressed solid argon were estimated for the first time, and the three-body interaction ab initio calculations were extended to a small distance. It shows that the four-body contribution is repulsive at high densities and effectively cancels the three-body lattice energy. The dimer potential plus three-body interaction can well reproduce the measurements of equation of state at pressure approximately lower than ∼60 GPa, when including the four-body effects extends the agreement up to the maximum experimental pressure of 114 GPa. PMID:26547175
NASA Astrophysics Data System (ADS)
Iqbal, A.; Toor, A. H.
2002-03-01
We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory, i.e., an evolutionarily stable strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.
NASA Astrophysics Data System (ADS)
Alaal, Naresh; Loganathan, Vaideesh; Medhekar, Nikhil; Shukla, Alok
2016-03-01
A first principles many-body approach is employed to calculate the band structure and optical response of nanometer-sized ribbons of SiC. Many-body effects are incorporated using the GW approximation, and excitonic effects are included using the Bethe–Salpeter equation. Both unpassivated and hydrogen-passivated armchair SiC nanoribbons are studied. As a consequence of low dimensionality, large quasiparticle corrections are seen to the Kohn–Sham energy gaps. In both cases quasiparticle band gaps are increased by up to 2 eV, as compared to their Kohn–Sham energy values. Inclusion of electron–hole interactions modifies the absorption spectra significantly, giving rise to strongly bound excitonic peaks in these systems. The results suggest that hydrogen passivated armchair SiC nanoribbons have the potential to be used in optoelectronic devices operating in the UV-Vis region of the spectrum. We also compute the formation energies of these nanoribbons as a function of their widths, and conclude that hydrogen-saturated ribbons will be much more stable as compared to bare ones.
Efficient free energy calculations of quantum systems through computer simulations
NASA Astrophysics Data System (ADS)
Antonelli, Alex; Ramirez, Rafael; Herrero, Carlos; Hernandez, Eduardo
2009-03-01
In general, the classical limit is assumed in computer simulation calculations of free energy. This approximation, however, is not justifiable for a class of systems in which quantum contributions for the free energy cannot be neglected. The inclusion of quantum effects is important for the determination of reliable phase diagrams of these systems. In this work, we present a new methodology to compute the free energy of many-body quantum systems [1]. This methodology results from the combination of the path integral formulation of statistical mechanics and efficient non-equilibrium methods to estimate free energy, namely, the adiabatic switching and reversible scaling methods. A quantum Einstein crystal is used as a model to show the accuracy and reliability the methodology. This new method is applied to the calculation of solid-liquid coexistence properties of neon. Our findings indicate that quantum contributions to properties such as, melting point, latent heat of fusion, entropy of fusion, and slope of melting line can be up to 10% of the calculated values using the classical approximation. [1] R. M. Ramirez, C. P. Herrero, A. Antonelli, and E. R. Hernández, Journal of Chemical Physics 129, 064110 (2008)
Short-time dynamics of correlated quantum Coulomb systems
NASA Astrophysics Data System (ADS)
Bonitz, Michael
2007-03-01
Strong correlations in dense Coulomb systems are attracting increasing interest in many fields ranging from dense astrophysical plasmas, dusty plasmas and semiconductors to metal clusters and ultracold trapped ions [1]. Examples are bound states in dense plasmas (atoms, molecules, clusters) and semiconductors (excitons, trions, biexcitons) and many-particle correlations such as Coulomb and Yukawa liquids and crystals. Of particular current interest is the response of these systems to short excitations generated e.g. by femtosecond laser pulses and giving rise to ultrafast relaxation processes and build up of binary correlations. The proper theoretical tool are non-Markovian quantum kinetic equations [1,2] which can be derived from Nonequilibrium Green's Functions (NEGF) and are now successfully solved numerically for dense plasmas and semiconductors [3], correlated electrons [4] and other many-body systems with moderate correlations [5]. This method is well suited to compute the nonlinear response to strong fields selfconsistently including many-body effects [6]. Finally, we discuss recent extensions of the NEGF-computations to the dynamics of strongly correlated Coulomb systems, such as single atoms and molecules [7] and electron and exciton Wigner crystals in quantum dots [8,9]. [1] H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer 1996; M. Bonitz Quantum Kinetic Theory, Teubner, Stuttgart/Leipzig 1998; [2] Progress in Nonequilibrium Green's Functions III, M. Bonitz and A. Filinov (Eds.), J. Phys. Conf. Ser. vol. 35 (2006); [3] M. Bonitz et al. Journal of Physics: Condensed Matter 8, 6057 (1996); R. Binder, H.S. K"ohler, and M. Bonitz, Phys. Rev. B 55, 5110 (1997); [4] N.H. Kwong, and M. Bonitz, Phys. Rev. Lett. 84, 1768 (2000); [5] Introduction to Computational Methods for Many-Body Systems, M. Bonitz and D. Semkat (eds.), Rinton Press, Princeton (2006); [6] H. Haberland, M. Bonitz, and D. Kremp, Phys. Rev. E 64, 026405 (2001); [7] N.E. Dahlen, A. Stan and R. van Leeuwen, p. 324 in Ref. 2.; [8] A. Filinov, M. Bonitz, and Yu. Lozovik, Phys. Rev. Lett. 86, 3851 (2001); [9] K. Balzer, N.E. Dahlen, R. van Leeuwen, and M. Bonitz, to be published
Classical command of quantum systems.
Reichardt, Ben W; Unger, Falk; Vazirani, Umesh
2013-04-25
Quantum computation and cryptography both involve scenarios in which a user interacts with an imperfectly modelled or 'untrusted' system. It is therefore of fundamental and practical interest to devise tests that reveal whether the system is behaving as instructed. In 1969, Clauser, Horne, Shimony and Holt proposed an experimental test that can be passed by a quantum-mechanical system but not by a system restricted to classical physics. Here we extend this test to enable the characterization of a large quantum system. We describe a scheme that can be used to determine the initial state and to classically command the system to evolve according to desired dynamics. The bipartite system is treated as two black boxes, with no assumptions about their inner workings except that they obey quantum physics. The scheme works even if the system is explicitly designed to undermine it; any misbehaviour is detected. Among its applications, our scheme makes it possible to test whether a claimed quantum computer is truly quantum. It also advances towards a goal of quantum cryptography: namely, the use of 'untrusted' devices to establish a shared random key, with security based on the validity of quantum physics. PMID:23619692
Quantum Effects in Biological Systems
NASA Astrophysics Data System (ADS)
Roy, Sisir
2014-07-01
The debates about the trivial and non-trivial effects in biological systems have drawn much attention during the last decade or so. What might these non-trivial sorts of quantum effects be? There is no consensus so far among the physicists and biologists regarding the meaning of "non-trivial quantum effects". However, there is no doubt about the implications of the challenging research into quantum effects relevant to biology such as coherent excitations of biomolecules and photosynthesis, quantum tunneling of protons, van der Waals forces, ultrafast dynamics through conical intersections, and phonon-assisted electron tunneling as the basis for our sense of smell, environment assisted transport of ions and entanglement in ion channels, role of quantum vacuum in consciousness. Several authors have discussed the non-trivial quantum effects and classified them into four broad categories: (a) Quantum life principle; (b) Quantum computing in the brain; (c) Quantum computing in genetics; and (d) Quantum consciousness. First, I will review the above developments. I will then discuss in detail the ion transport in the ion channel and the relevance of quantum theory in brain function. The ion transport in the ion channel plays a key role in information processing by the brain.
Quantum technologies with hybrid systems.
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-03-31
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field. PMID:25737558
Quantum technologies with hybrid systems
Kurizki, Gershon; Bertet, Patrice; Kubo, Yuimaru; Mølmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, Jörg
2015-01-01
An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near- and long-term perspectives of this fascinating and rapidly expanding field. PMID:25737558
Hypervirial approach to calculating expectation values of the many-body Hamiltonian
NASA Astrophysics Data System (ADS)
Adam, R. M.; Fiedeldey, H.
1995-05-01
We present a new method, based on the hypervirial operator, for calculating expectation values of many-body Hamiltonians for local velocity-independent potentials. Our approach enables us to calculate the contributions of different components of an interaction [e.g., tensor, one pion exchange part (OPEP)] to the binding energy when all components are acting. In particular, using the integro-differential equation approach we investigate the contributions of different components of realistic nucleon-nucleon potentials to the triton and α particle ground-state binding energies. Although the tensor force contributes the most to the expectation value of the potential energy, we find that its overall contribution to the binding energy is much reduced by its large contribution to the expectation value of the kinetic energy.
Many-body treatment of white dwarf and neutron stars on the brane
Azam, Mofazzal; Sami, M.
2005-07-15
Brane-world models suggest modification of Newton's law of gravity on the 3-brane at submillimeter scales. The brane-world induced corrections are in higher powers of inverse distance and appear as additional terms with the Newtonian potential. The average interparticle distance in white dwarf and neutron stars is 10{sup -10} cms and 10{sup -13} cms, respectively, and therefore, the effect of submillimeter corrections needs to be investigated. We show, by carrying out simple many-body calculations, that the mass and mass-radius relationship of the white dwarf and neutron stars are not effected by submillimeter corrections. However, our analysis shows that the correction terms in the effective theory give rise to force akin to surface tension in normal liquids.
Ab Initio Many-Body Calculations Of Nucleon-Nucleus Scattering
Quaglioni, S; Navratil, P
2008-12-17
We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and Pauli principle. We outline technical details and present phase shift results for neutron scattering on {sup 3}H, {sup 4}He and {sup 10}Be and proton scattering on {sup 3,4}He, using realistic nucleon-nucleon (NN) potentials. Our A = 4 scattering results are compared to earlier ab initio calculations. We find that the CD-Bonn NN potential in particular provides an excellent description of nucleon-{sup 4}He S-wave phase shifts. We demonstrate that a proper treatment of the coupling to the n-{sup 10}Be continuum is successful in explaining the parity-inverted ground state in {sup 11}Be.
Second-order many-body perturbation study of ice Ih
He, Xiao; Sode, Olaseni; Xantheas, Sotiris S.; Hirata, So
2012-11-28
Ice Ih is arguably the most important molecular crystal in nature, yet our understanding of its structural and dynamical properties is still incomplete. To explain the origin of two peaks in the hydrogen-bond-stretching region of the inelastic neutron scattering (INS) spectra, the existence of two types of hydrogen bonds with strengths differing by a factor of two was previously hypothesized. We present first-principles calculations based on diagrammatic many-body perturbation theory of the structures and vibrational spectra of ice Ih, which suggest that the observed spectral features arise from the directionality or anisotropy of the hydrogen-bond stretching vibrations rather than their vastly different force constants, disproving the previous hypothesis. Our calculations also reproduce the infrared and Raman spectra, the variation of INS spectra with deuterium concentration, and the anomaly of heat capacities at low temperatures, together rendering our calculations a paradigm for "crystals from first principles" as envisioned by Maddox.
NASA Astrophysics Data System (ADS)
Monserrat, Bartomeu
2016-03-01
A method is proposed for the inclusion of electron correlation in the calculation of the temperature dependence of band structures arising from electron-phonon coupling. It relies on an efficient exploration of the vibrational phase space along the recently introduced thermal lines. Using the G0W0 approximation, the temperature dependence of the direct gaps of diamond, silicon, lithium fluoride, magnesium oxide, and titanium dioxide is calculated. Within the proposed formalism, a single calculation at each temperature of interest is sufficient to obtain results of the same accuracy as in alternative, more expensive methods. It is shown that many-body contributions beyond semilocal density functional theory modify the electron-phonon coupling strength by almost 50 % in diamond, silicon, and titanium dioxide, but by less than 5 % in lithium flouride and magnesium oxide. The results reveal a complex picture regarding the validity of semilocal functionals for the description of electron-phonon coupling.
Out-of-equilibrium states and quasi-many-body localization in polar lattice gases
NASA Astrophysics Data System (ADS)
Barbiero, L.; Menotti, C.; Recati, A.; Santos, L.
2015-11-01
The absence of energy dissipation leads to an intriguing out-of-equilibrium dynamics for ultracold polar gases in optical lattices, characterized by the formation of dynamically bound on-site and inter-site clusters of two or more particles, and by an effective blockade repulsion. These effects combined with the controlled preparation of initial states available in cold-gas experiments can be employed to create interesting out-of-equilibrium states. These include quasiequilibrated effectively repulsive 1D gases for attractive dipolar interactions and dynamically bound crystals. Furthermore, nonequilibrium polar lattice gases can offer a promising scenario for the study of quasi-many-body localization in the absence of quenched disorder. This fascinating out-of-equilibrium dynamics for ultracold polar gases in optical lattices may be accessible in on-going experiments.
Shu, Huabing; Wang, Shudong; Li, Yunhai; Yip, Joanne; Wang, Jinlan
2014-08-14
The electronic structure and optical response of silicane to strain are investigated by employing first-principles calculations based on many-body perturbation theory. The bandgap can be efficiently engineered in a broad range and an indirect to direct bandgap transition is observed under a strain of 2.74%; the semiconducting silicane can even be turned into a metal under a very large strain. The transitions derive from the persistent downward shift of the lowest conduction band at the Γ-point upon an increasing strain. The quasi-particle bandgaps of silicane are sizable due to the weak dielectric screening and the low dimension; they are rapidly reduced as strain increases while the exciton bound energy is not that sensitive. Moreover, the optical absorption edge of the strained silicane significantly shifts towards a low photon energy region and falls into the visible light range, which might serve as a promising candidate for optoelectronic devices. PMID:25134590
Three-particle correlation from a Many-Body Perspective: Trions in a Carbon Nanotube
NASA Astrophysics Data System (ADS)
Deilmann, Thorsten; Drüppel, Matthias; Rohlfing, Michael
2016-05-01
Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab initio approach. It can be regarded as an extension of the widely used G W method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are redshifted by ˜130 meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions.
NASA Astrophysics Data System (ADS)
Huda, M. N.; Ray, A. K.
2003-03-01
The formalism of second order many body perturbation theory has been applied to investigate the electronic and geometric structures of neutral, cationic, and anionic Agn (n=5-9) clusters. Hay-Wadt relativistic effective core potentials replacing the twenty-eight core electrons and a Gaussian basis set have been used. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. The neutral silver clusters prefer planar geometry up to n=6 and the charged clusters prefer three dimensional geometry from n=6. Binding energies, ionization potentials, electron affinities, and fragmentation energies of the optimized clusters have been compared with other experimental and theoretical results available in the literature. Based on different criteria, we predict the eight-atom silver cluster to be a magic cluster. * Work supported in part by the Welch Foundation, Houston, Texas (Grant No. Y-1525) 1 M. N. Huda and A. K. Ray, Phys. Rev. A, in press.
Charmonium, Glueballs and Exotic Hybrids in a Relativistic Many-Body Approach
NASA Astrophysics Data System (ADS)
Cotanch, Stephen R.
2001-10-01
Utilizing conventional many-body techniques, an effective QCD Hamiltonian formulated in the Coulomb gauge is approximately diagonalized. This approach preserves chiral symmetry yet generates constituents with dynamical mass confined through a linear potential with slope specified by lattice gauge theory. The experimental meson and lattice glueball spectra are reasonably described and exhibit Regge trajectories consistent with observation including the Pomeron. A fully relativistic, three quasiparticle calculation for hybrid mesons reinforces alternative theoretical models and predicts the lightest hybrid states are near but above 2 GeV. This strongly suggests the recently observed JPC = 1-+ exotics at 1.4 and 1.6 GeV are of a different, perhaps four quark, structure. Charmonium predictions now resolve the overpopulation of J/? states relative to observation. Extensions and preliminary results for low energy ?? scattering are also discussed.
Electronic structure of assembled graphene nanoribbons: Substrate and many-body effects
NASA Astrophysics Data System (ADS)
Liang, Liangbo; Meunier, Vincent
2012-11-01
Experimentally measured electronic band gaps of atomically sharp straight and chevronlike armchair graphene nanoribbons (GNRs) adsorbed on a gold substrate are smaller than theoretically predicted quasiparticle band gaps of their free-standing counterparts [Linden , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.216801 108, 216801 (2012)]. The influence of the substrate on electronic properties of both straight and chevronlike GNRs is here investigated including many-body effects beyond semilocal density-functional theory. The predicted small electron transfer from a straight or chevronlike GNR to the gold surface is found to lead to a surface polarization at the GNR-metal interface responsible for a significant reduction of the quasiparticle band gap of the GNR. This reduction is quantified using a semiclassical image charge model. By considering both quasiparticle and surface polarization corrections, we obtain theoretical band gaps that are consistent with experimental ones for gold-supported GNRs.
Regularizing the molecular potential in electronic structure calculations. II. Many-body methods
Bischoff, Florian A.
2014-11-14
In Paper I of this series [F. A. Bischoff, “Regularizing the molecular potential in electronic structure calculations. I. SCF methods,” J. Chem. Phys. 141, 184105 (2014)] a regularized molecular Hamilton operator for electronic structure calculations was derived and its properties in SCF calculations were studied. The regularization was achieved using a correlation factor that models the electron-nuclear cusp. In the present study we extend the regularization to correlated methods, in particular the exact solution of the two-electron problem, as well as second-order many body perturbation theory. The nuclear and electronic correlation factors lead to computations with a smaller memory footprint because the singularities are removed from the working equations, which allows coarser grid resolution while maintaining the precision. Numerical examples are given.
Willow, Soohaeng Yoo; Center for Superfunctional Materials, Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784 ; Zhang, Jinmei; Valeev, Edward F.; Hirata, So; CREST, Japan Science and Technology Agency, Saitama 332-0012
2014-01-21
A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H{sub 2}O, CH{sub 4}, and C{sub 6}H{sub 6} within a few mE{sub h} after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.
The ionization potential of aqueous hydroxide computed using many-body perturbation theory
Opalka, Daniel Sprik, Michiel; Pham, Tuan Anh; Galli, Giulia
2014-07-21
The ionization potentials of electrolyte solutions provide important information about the electronic structure of liquids and solute-solvent interactions. We analyzed the positions of solute and solvent bands of aqueous hydroxide and the influence of the solvent environment on the ionization potential of hydroxide ions. We used the concept of a computational hydrogen electrode to define absolute band positions with respect to vacuum. We found that many-body perturbation theory in the G{sub 0} W{sub 0} approximation substantially improves the relative and absolute positions of the band edges of solute and solvent with respect to those obtained within Density Functional Theory, using semi-local functionals, yielding results in satisfactory agreement with recent experiments.
Shu, Huabing; Wang, Shudong; Li, Yunhai; Wang, Jinlan; Yip, Joanne
2014-08-14
The electronic structure and optical response of silicane to strain are investigated by employing first-principles calculations based on many-body perturbation theory. The bandgap can be efficiently engineered in a broad range and an indirect to direct bandgap transition is observed under a strain of 2.74%; the semiconducting silicane can even be turned into a metal under a very large strain. The transitions derive from the persistent downward shift of the lowest conduction band at the Γ-point upon an increasing strain. The quasi-particle bandgaps of silicane are sizable due to the weak dielectric screening and the low dimension; they are rapidly reduced as strain increases while the exciton bound energy is not that sensitive. Moreover, the optical absorption edge of the strained silicane significantly shifts towards a low photon energy region and falls into the visible light range, which might serve as a promising candidate for optoelectronic devices.
Quantum models of classical systems
NASA Astrophysics Data System (ADS)
Hj?ek, P.
2015-07-01
Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties.
Decoherence in infinite quantum systems
Blanchard, Philippe; Hellmich, Mario
2012-09-01
We review and discuss a notion of decoherence formulated in the algebraic framework of quantum physics. Besides presenting some sufficient conditions for the appearance of decoherence in the case of Markovian time evolutions we provide an overview over possible decoherence scenarios. The framework for decoherence we establish is sufficiently general to accommodate quantum systems with infinitely many degrees of freedom.
Coulomb crystallization in classical and quantum systems
NASA Astrophysics Data System (ADS)
Bonitz, Michael
2007-11-01
Coulomb crystallization occurs in one-component plasmas when the average interaction energy exceeds the kinetic energy by about two orders of magnitude. A simple road to reach such strong coupling consists in using external confinement potentials the strength of which controls the density. This has been succsessfully realized with ions in traps and storage rings and also in dusty plasma. Recently a three-dimensional spherical confinement could be created [1] which allows to produce spherical dust crystals containing concentric shells. I will give an overview on our recent results for these ``Yukawa balls'' and compare them to experiments. The shell structure of these systems can be very well explained by using an isotropic statically screened pair interaction. Further, the thermodynamic properties of these systems, such as the radial density distribution are discussed based on an analytical theory [3]. I then will discuss Coulomb crystallization in trapped quantum systems, such as mesoscopic electron and electron hole plasmas in coupled layers [4,5]. These systems show a very rich correlation behavior, including liquid and solid like states and bound states (excitons, biexcitons) and their crystals. On the other hand, also collective quantum and spin effects are observed, including Bose-Einstein condensation and superfluidity of bound electron-hole pairs [4]. Finally, I consider Coulomb crystallization in two-component neutral plasmas in three dimensions. I discuss the necessary conditions for crystals of heavy charges to exist in the presence of a light component which typically is in the Fermi gas or liquid state. It can be shown that their exists a critical ratio of the masses of the species of the order of 80 [5] which is confirmed by Quantum Monte Carlo simulations [6]. Familiar examples are crystals of nuclei in the core of White dwarf stars, but the results also suggest the existence of other crystals, including proton or α-particle crystals in dense matter and of hole crystals in semiconductors. [1] O. Arp, D. Block, A. Piel, and A. Melzer, Phys. Rev. Lett. 93, 165004 (2004). [2] M. Bonitz, D. Block, O. Arp, V. Golubnychiy, H. Baumgartner, P. Ludwig, A. Piel, and A. Filinov, Phys. Rev. Lett. 96, 075001 (2006). [3] C. Henning, H. Baumgartner, A. Piel, P. Ludwig, V. Golubnychiy, M. Bonitz, and D. Block, Phys. Rev. E 74, 056403 (2006) and Phys. Rev. E (2007). [4] A. Filinov, M. Bonitz, and Yu. Lozovik, Phys. Rev. Lett. 86, 3851 (2001). [5] M. Bonitz, V. Filinov, P. Levashov, V. Fortov, and H. Fehske, Phys. Rev. Lett. 95, 235006 (2005) and J. Phys. A: Math. Gen. 39, 4717 (2006). [6] Introduction to Computational Methods for Many-Body Systems, M. Bonitz and D. Semkat (eds.), Rinton Press, Princeton (2006)
Desgranges, Caroline; Delhommelle, Jerome
2016-03-28
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si. PMID:27036464
NASA Astrophysics Data System (ADS)
Desgranges, Caroline; Delhommelle, Jerome
2016-03-01
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.