Seniority in quantum many-body systems
Van Isacker, P.
2010-12-23
The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-j shell, its extension to the case of many, non-degenerate j shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose-Einstein condensates of atoms with spin.
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, RÃ©nyi 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.
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
Measure synchronization in quantum many-body systems
NASA Astrophysics Data System (ADS)
Qiu, Haibo; Juliá-Díaz, Bruno; Garcia-March, Miguel Angel; Polls, Artur
2014-09-01
The concept of measure synchronization between two coupled quantum many-body systems is presented. In general terms we consider two quantum many-body systems whose dynamics gets coupled through the contact particle-particle interaction. This coupling is shown to produce measure synchronization, a generalization of synchrony to a large class of systems which takes place in absence of dissipation. We find that in quantum measure synchronization, the many-body quantum properties for the two subsystems, e.g., condensed fractions and particle fluctuations, behave in a coordinated way. To illustrate the concept we consider a simple case of two species of bosons occupying two distinct quantum states. Measure synchronization can be readily explored with state-of-the-art techniques in ultracold atomic gases and, if properly controlled, be employed to build targeted quantum correlations in a sympathetic way.
Simulation of Strongly Correlated Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Bilgin, Ersen
In this thesis, we address the problem of solving for the properties of interacting quantum many-body systems in thermal equilibrium. The complexity of this problem increases exponentially with system size, limiting exact numerical simulations to very small systems. To tackle more complex systems, one needs to use heuristic algorithms that approximate solutions to these systems. Belief propagation is one such algorithm that we discuss in chapters 2 and 3. Using belief propagation, we demonstrate that it is possible to solve for static properties of highly correlated quantum many-body systems for certain geometries at all temperatures. In chapter 4, we generalize the multiscale renormalization ansatz to the anyonic setting to solve for the ground state properties of anyonic quantum many-body systems. The algorithms we present in chapters 2, 3, and 4 are very successful in certain settings, but they are not applicable to the most general quantum mechanical systems. For this, we propose using quantum computers as we discuss in chapter 5. The dimension reduction algorithm we consider in chapter 5 enables us to prepare thermal states of any quantum many-body system on a quantum computer faster than any previously known algorithm. Using these thermal states as the initialization of a quantum computer, one can study both static and dynamic properties of quantum systems without any memory overhead.
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
Boundary driven open quantum many-body systems
Prosen, TomaÅ¾
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.
Conditional independence in quantum many-body systems
NASA Astrophysics Data System (ADS)
Kim, Isaac Hyun
In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.
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.
Unifying variational methods for simulating quantum many-body systems.
Dawson, C M; Eisert, J; Osborne, T J
2008-04-01
We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations, inspired by flow equation methods. Variational classes are represented as efficiently contractible unitary networks, including the matrix-product states of density matrix renormalization, multiscale entanglement renormalization (MERA) states, weighted graph states, and quantum cellular automata. In particular, this provides a tool for varying over classes of states, such as MERA, for which so far no efficient way of variation has been known. The scheme is flexible when it comes to hybridizing methods or formulating new ones. We demonstrate the functioning by numerical implementations of MERA, matrix-product states, and a new variational set on benchmarks. PMID:18517924
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, Tomáš; 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 Poincaré 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; SchirÃ³, 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
Quantum effects in many-body gravitating systems
NASA Astrophysics Data System (ADS)
Golovko, V. A.
2005-07-01
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this number equals Avogadro's number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the atmosphere decreases as its mass increases. If short-range intermolecular forces are taken into account, the results obtained hold for excited states whose lifetime can however be very long. The results of the paper can be utilized for explaining the first stage of formation of celestial bodies from interstellar and even intergalactic gases.
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
Quantum simulation. Coherent imaging spectroscopy of a quantum many-body spin system.
Senko, C; Smith, J; Richerme, P; Lee, A; Campbell, W C; Monroe, C
2014-07-25
Quantum simulators, in which well-controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics inaccessible to modeling with classical computers. However, checking the results of such simulations also becomes classically intractable as system sizes increase. Here, we introduce and implement a coherent imaging spectroscopic technique, akin to magnetic resonance imaging, to validate a quantum simulation. We use this method to determine the energy levels and interaction strengths of a fully connected quantum many-body system. Additionally, we directly measure the critical energy gap near a quantum phase transition. We expect this general technique to become a verification tool for quantum simulators once experiments advance beyond proof-of-principle demonstrations and exceed the resources of conventional computers. PMID:25061207
Quantum many-body system based on phonons and donors in silicon
NASA Astrophysics Data System (ADS)
Soykal, Ö. O.; Tahan, Charles
2012-02-01
Cold atoms in optical lattices have become an indispensable tool for the study of many-body physics. Here, we introduce a novel many-body quantum system based on phonons with potentially useful properties. Theoretical results will be presented on the possibility of interacting systems based on phonitons, hybrid composite objects of a matter excitation and a cavity phonon. We discuss experimentally accessible regimes in silicon phoniton systems involving Mott insulator and superfluid phases. We consider experimental tools to probe these many-body states and give explicit designs for devices where they can be observed.
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.
Light-cone-like spreading of correlations in a quantum many-body system.
Cheneau, Marc; Barmettler, Peter; Poletti, Dario; Endres, Manuel; Schauss, Peter; Fukuhara, Takeshi; Gross, Christian; Bloch, Immanuel; Kollath, Corinna; Kuhr, Stefan
2012-01-26
In relativistic quantum field theory, information propagation is bounded by the speed of light. No such limit exists in the non-relativistic case, although in real physical systems, short-range interactions may be expected to restrict the propagation of information to finite velocities. The question of how fast correlations can spread in quantum many-body systems has been long studied. The existence of a maximal velocity, known as the Lieb-Robinson bound, has been shown theoretically to exist in several interacting many-body systems (for example, spins on a lattice)--such systems can be regarded as exhibiting an effective light cone that bounds the propagation speed of correlations. The existence of such a 'speed of light' has profound implications for condensed matter physics and quantum information, but has not been observed experimentally. Here we report the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open perspectives for understanding the relaxation of closed quantum systems far from equilibrium, and for engineering the efficient quantum channels necessary for fast quantum computations. PMID:22281597
Measuring entanglement entropy of a generic many-body system with a quantum switch.
Abanin, Dmitry A; Demler, Eugene
2012-07-13
Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Rényi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order. PMID:23030142
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 physicsâ€”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.
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.
Variational principle for steady states of dissipative quantum many-body systems.
Weimer, Hendrik
2015-01-30
We present a novel generic framework to approximate the nonequilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the dynamics. We show how to apply this approach to different classes of variational quantum states and demonstrate its successful application to a dissipative extension of the Ising model, which is of importance to ongoing experiments on ultracold Rydberg atoms, as well as to a driven-dissipative variant of the Bose-Hubbard model. Finally, we identify several advantages of the variational approach over previously employed mean-field-like methods. PMID:25679882
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.
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-SÃ©bastien 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-1â„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 JukiÄ‡ 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
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 RÃ©nyi 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 RÃ©nyi 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.
Spin, angular momentum and spin-statistics for a relativistic quantum many-body system
NASA Astrophysics Data System (ADS)
Horwitz, Lawrence
2013-01-01
The adaptation of Wigner’s induced representation for a relativistic quantum theory making possible the construction of wave packets and admitting covariant expectation values for the coordinate operator x? introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch-Gordan coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many-body systems and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are briefly discussed. This paper is dedicated to the memory of Constantin Piron.
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.
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.
Measuring the dynamic structure factor of a dissipative quantum many-body system
NASA Astrophysics Data System (ADS)
Donner, Tobias; Landig, Renate; Mottl, Rafael; Hruby, Lorenz; Brennecke, Ferdinand; Esslinger, Tilman
2014-05-01
A Bose-Einstein condensate whose motional degrees of freedom are coupled to a high-finesse optical cavity via a transverse pump beam constitutes a dissipative quantum many-body system with long range interactions. These interactions can induce a structural phase transition from a flat to a density-modulated state. The transverse pump field simultaneously represents a probe of the atomic density via cavity-enhanced Bragg scattering. By spectrally analysing the light field leaking out of the cavity, we measure non-destructively the dynamic structure factor of the fluctuating atomic density while the system undergoes the phase transition. An observed asymmetry in the dynamic structure factor is attributed to the coupling to dissipative baths. Critical exponents for both sides of the phase transition can be extracted from the data. We further discuss our progress in adding strong short-range interactions to this system, in order to explore Bose-Hubbard physics with cavity-mediated long-range interactions and self-organization in lower dimensions.
Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system
NASA Astrophysics Data System (ADS)
Bouvrie, Peter A.; Majtey, Ana P.; Tichy, Malte C.; Dehesa, Jesus S.; Plastino, Angel R.
2014-11-01
We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons." We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view.
Entanglement patterns and generalized correlation functions in quantum many-body systems
NASA Astrophysics Data System (ADS)
Barcza, G.; Noack, R. M.; Sólyom, J.; Legeza, Ö.
2015-09-01
We introduce transition operators that in a given basis of the single-site states of a many-body system have a single nonvanishing matrix element and introduce their correlation functions. We show that they fall into groups that decay with the same rate. The mutual information defined in terms of the von Neumann entropy between two sites is given in terms of these so-called generalized correlation functions. We confirm numerically that the long-distance decay of the mutual information follows the square of that of the most slowly decaying generalized correlation function. The main advantage of our procedure is that, in order to identify the most relevant physical processes, there is no need to know a priori the nature of the ordering in the system, i.e., no need to explicitly construct particular physical correlation functions. We explore the behavior of the mutual information and the generalized correlation functions for comformally invariant models and for the SU(n ) Hubbard model with n =2 ,3 ,4 , and 5, which are, in general, not conformally invariant. In this latter case, we show that for filling f =1 /q and q
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.
Distributed thermal tasks on many-body systems through a single quantum machine
NASA Astrophysics Data System (ADS)
Leggio, Bruno; Doyeux, Pierre; Messina, Riccardo; Antezza, Mauro
2015-11-01
We propose a configuration of a single three-level quantum emitter embedded in a non-equilibrium steady electromagnetic environment, able to stabilize and control the local temperatures of a target system it interacts with, consisting of a collection of coupled two-level systems. The temperatures are induced by dissipative processes only, without the need of further external couplings for each qubit. Moreover, by acting on a set of easily tunable geometric parameters, we demonstrate the possibility to manipulate and tune each qubit temperature independently over a remarkably broad range of values. These findings address one standard problem in quantum-scale thermodynamics, providing a way to induce a desired distribution of temperature among interacting qubits and to protect it from external noise sources.
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 excitonâ€“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 excitonâ€“phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Quantum nonlocality. Detecting nonlocality in many-body quantum states.
Tura, J; Augusiak, R; Sainz, A B; Vértesi, T; Lewenstein, M; Acín, A
2014-06-13
Intensive studies of entanglement properties have proven essential for our understanding of quantum many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems because the available multipartite Bell inequalities involve correlations among many particles, which are difficult to access experimentally. We constructed multipartite Bell inequalities that involve only two-body correlations and show how they reveal the nonlocality in many-body systems relevant for nuclear and atomic physics. Our inequalities are violated by any number of parties and can be tested by measuring total spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles. PMID:24926014
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 states—a 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.
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)
Donner, Tobias
2015-03-01
A Bose-Einstein condensate whose motional degrees of freedom are coupled to a high-finesse optical cavity via a transverse pump beam constitutes a dissipative quantum many-body system with long range interactions. These interactions can induce a structural phase transition from a flat to a density-modulated state. The transverse pump field simultaneously represents a probe of the atomic density via cavity- enhanced Bragg scattering. By spectrally analyzing the light field leaking out of the cavity, we measure non-destructively the dynamic structure factor of the fluctuating atomic density while the system undergoes the phase transition. An observed asymmetry in the dynamic structure factor is attributed to the coupling to dissipative baths. Critical exponents for both sides of the phase transition can be extracted from the data. We further discuss our progress in adding strong short-range interactions to this system, in order to explore Bose-Hubbard physics with cavity-mediated long-range interactions and self-organization in lower dimensions.
Semiclassical Methods for Many-Body Systems
NASA Astrophysics Data System (ADS)
Landry, Brian Robert
Semiclassical methods are some of the most effective for tackling the notorious many-body problem. We follow up on some inspired work in the field of semiclassical physics including the Berry random wave conjecture and its connection to statistical mechanics, and the Thomas-Fermi approximation. The main thrust of the work is a new semiclassical method based on the Thomas-Fermi approximation that shows positive results especially for highly correlated systems. A new way of looking at particle exchange symmetry is central to our new method, and as such we take a fresh look at permutation symmetry in many-body systems of identical particles.
Many body effects in atomic systems
NASA Astrophysics Data System (ADS)
Fu, Hao
2007-12-01
This thesis summarizes work on the theory of many-body effects in atomic systems. The modification of emission rates and spectra for a single impurity atom embedded in a many-body system is studied. In addition, the physics of two, cold atom systems is investigated. We first study the spontaneous decay of a source atom inside a dielectric. In a microscopic picture, the photon radiated by the source atom is scattered by the medium atoms. This scattered photon is absorbed by the source atom, which results in a modification of the atom's decay rate. The calculation is carried out to second order in the medium density and we find a result that differs from the one obtained in macroscopic calculations. Using the same microscopic model, we carry out a microscopic calculation for the recoil momentum acquired by a radiating atom in a medium. In our microscopic calculation, the average value of the photon momentum is modified by its scattering with the source atoms. This gives a modification to the recoil momentum of the source atom. The calculated correction agrees with the experimental observations. In the second part of the thesis, we study two, ultra-cold atomic systems. An exactly solvable model, a Tonks-Girardeau gas with a local potential, is explained first. Such a one dimensional quantum gas has been realized recently. The spectrum of the single particle density matrix is evaluated exactly. We find the "condensate density" as a function of the potential strength. We also propose to use time-of-flight imaging to detect experimental observables. The possibility of modulating the interaction strength in space using a Feshbach resonance in a degenerate Fermi gas is examined in the last part of the thesis. Using a periodic modulation, we find that the ground state of the system contains Cooper pairs with non-zero center-of-mass momenta. The resultant single particle spectrum is found to have an additional gap along particular directions. We propose experimental schemes to detect properties of both the ground state and the quasi-particle excitations.
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
NASA Astrophysics Data System (ADS)
Esler, Kenneth Paul
Path integral Monte Carlo (PIMC) is a quantum-level simulation method based on a stochastic sampling of the many-body thermal density matrix. Utilizing the imaginary-time formulation of Feynman's sum-over-histories, it includes thermal fluctuations and particle correlations in a natural way. Over the past two decades, PIMC has been applied to the study of the electron gas, hydrogen under extreme pressure, and superfluid helium with great success. However, the computational demand scales with a high power of the atomic number, preventing its application to systems containing heavier elements. In this dissertation, we present the methodological developments necessary to apply this powerful tool to these systems. We begin by introducing the PIMC method. We then explain how effective potentials with position-dependent electron masses can be used to significantly reduce the computational demand of the method for heavier elements, while retaining high accuracy. We explain how these pseudohamiltonians can be integrated into the PIMC simulation by computing the density matrix for the electron-ion pair. We then address the difficulties associated with the long-range behavior of the coulomb potential, and improve a method to optimally partition particle interactions into real-space and reciprocal-space summations. We discuss the use of twist-averaged boundary conditions to reduce the finite-size effects in our simulations and the fixed-phase method needed to enforce the boundary conditions. Finally, we explain how a PIMC simulation of the electrons can be coupled to a classical Langevin dynamics simulation of the ions to achieve an efficient sampling of all degrees of freedom. After describing these advancements in methodology, we apply our new technology to fluid sodium near its liquid-vapor critical point. In particular, we explore the microscopic mechanisms which drive the continuous change from a dense metallic liquid to an expanded insulating vapor above the critical temperature. We show that the dynamic aggregation and dissociation of clusters of atoms play a significant role in determining the conductivity and that the formation of these clusters is highly density and temperature dependent. Finally, we suggest several avenues for research to further improve our simulations.
Benet, L.; Chadderton, L. T.; Kun, S. Yu.; Qi Wang
2007-06-15
We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D{sub 2} chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.
Many-Body Localization in Dipolar Systems
NASA Astrophysics Data System (ADS)
Yao, N. Y.; Laumann, C. R.; Gopalakrishnan, S.; Knap, M.; Müller, 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.
Many-body localization in dipolar systems.
Yao, N Y; Laumann, C R; Gopalakrishnan, S; Knap, M; MÃ¼ller, 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
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
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.
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 HÃ¼bener, V Nebendahl and W DÃ¼r 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, RomÃ¡n OrÃºs, John Ove FjÃ¦restad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D PÃ©rez-GarcÃa, M Sanz, C E GonzÃ¡lez-GuillÃ©n, 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 TomaÅ¾ Prosen and Bojan Å½unkoviÄ 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 MÃ¼nder, 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 LÃ¤uchli, 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 GarcÃa-Saez and A AcÃn 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 relationsâ€”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 HÃ¼bener, 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.
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; PapiÄ‡, 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.
Scattering approach to quantum transport and many body effects
Pichard, Jean-Louis
2010-12-21
We review a series of works discussing how the scattering approach to quantum transport developed by Landauer and Buttiker for one body elastic scatterers can be extended to the case where electron-electron interactions act inside the scattering region and give rise to many body scattering. Firstly, we give an exact numerical result showing that at zero temperature a many body scatterer behaves as an effective one body scatterer, with an interaction dependent transmission. Secondly, we underline that this effective scatterer depends on the presence of external scatterers put in its vicinity. The implications of this non local scattering are illustrated studying the conductance of a quantum point contact where electrons interact with a scanning gate microscope. Thirdly, using the numerical renormalization group developed by Wilson for the Kondo problem, we study a double dot spinless model with an inter-dot interaction U and inter-dot hopping t{sub d}, coupled to leads by hopping terms t{sub c}. We show that the quantum conductance as a function of t{sub d} is given by a universal function, independently of the values of U and t{sub c}, if one measures t{sub d} in units of a characteristic scale {tau}(U,t{sub c}). Mapping the double dot system without spin onto a single dot Anderson model with spin and magnetic field, we show that {tau}(U,t{sub c}) 2T{sub K}, where T{sub K} is the Kondo temperature of the Anderson model.
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.
Roux, Guillaume
2010-09-15
In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expected thermalization scenario discussed by Rigol. In addition, we emphasize a few other important aspects, in particular the definition of temperature and the equivalence of ensemble, which are much more difficult to show numerically even though we believe they are essential to the discussion of thermalization. These remarks could be of interest to people interested in the interpretation of the data obtained on finite-size systems.
Many-body spin systems with ultracold polar KRb molecules
NASA Astrophysics Data System (ADS)
Covey, Jacob; Gadway, Bryce; Yan, Bo; Moses, Steven; Jin, Deborah; Ye, Jun
2014-05-01
Long-range dipolar interactions are expected to facilitate understanding of strongly correlated many-body quantum systems such as quantum magnetism. We have used dipolar interactions of polar molecules pinned in a three-dimensional optical lattice to realize a lattice spin model where spin is encoded in rotational states of molecules that are prepared and probed by microwaves. The many-body dipolar interactions are apparent in the evolution of the spin coherence, which shows oscillations in addition to an overall decay of the coherence. The frequency of these oscillations depends on the strength of the dipolar interaction, which we can vary, and agrees quantitatively with a dipolar spin-exchange model. However, the absence of an external electric field precludes the study of the full spin-1/2 Hamiltonian that includes the Ising interaction. We are now building a novel apparatus that will allow us to reach large electric fields with full tunability of the relative strength of the Ising and exchange terms. Moreover, we anticipate imaging our sample with a high-NA microscope objective, allowing microscopic studies of a many-body spin system of polar molecules.
Many-body energy localization transition in periodically driven systems
Dâ€™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 (Fermiâ€“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: â€¢A dynamical localization transition in periodically driven ergodic systems is found. â€¢This phenomenon is reminiscent of many-body localization in energy space. â€¢Our results are valid for classical and quantum systems in the thermodynamic limit. â€¢At critical frequency, the short time expansion for the evolution operator breaks down. â€¢The transition is associated to a divergent time scale.
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].
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.
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.
Measuring entanglement entropies in many-body systems
Klich, Israel; Refael, Gil; Silva, Alessandro
2006-09-15
We explore the relation between entanglement entropy of quantum many-body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that, in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, XY spin chain, and chains with strong randomness.
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.
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.
Ideal quantum glass transitions: Many-body localization without quenched disorder
Schiulaz, M.; MÃ¼ller, 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.
Determinant method and quantum simulations of many-body effects in a single impurity Anderson model
Gubernatis, J.E.; Olson, T.C.; Scalapino, D.J.; Sugar, R.L.
1986-06-01
We present a short description of a quantum Monte Carlo technique that has proved useful for simulating many-body effects in systems of interacting fermins at finite temperatures. We then report our preliminary results using this technique on a single impurity Anderson model. Examples of such many-body effects as local moment formation, Kondo behavior, and mixed valence phenomena found in the simulations are shown.
Exponentially Slow Heating in Periodically Driven Many-Body Systems.
Abanin, Dmitry A; De Roeck, Wojciech; Huveneers, FranÃ§ois
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
Petascale Many Body Methods for Complex Correlated Systems
NASA Astrophysics Data System (ADS)
Pruschke, Thomas
2012-02-01
Correlated systems constitute an important class of materials in modern condensed matter physics. Correlation among electrons are at the heart of all ordering phenomena and many intriguing novel aspects, such as quantum phase transitions or topological insulators, observed in a variety of compounds. Yet, theoretically describing these phenomena is still a formidable task, even if one restricts the models used to the smallest possible set of degrees of freedom. Here, modern computer architectures play an essential role, and the joint effort to devise efficient algorithms and implement them on state-of-the art hardware has become an extremely active field in condensed-matter research. To tackle this task single-handed is quite obviously not possible. The NSF-OISE funded PIRE collaboration ``Graduate Education and Research in Petascale Many Body Methods for Complex Correlated Systems'' is a successful initiative to bring together leading experts around the world to form a virtual international organization for addressing these emerging challenges and educate the next generation of computational condensed matter physicists. The collaboration includes research groups developing novel theoretical tools to reliably and systematically study correlated solids, experts in efficient computational algorithms needed to solve the emerging equations, and those able to use modern heterogeneous computer architectures to make then working tools for the growing community.
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.
Many-Body Localization in Periodically Driven Systems
NASA Astrophysics Data System (ADS)
Ponte, Pedro; Papi?, Z.; Huveneers, François; Abanin, Dmitry A.
2015-04-01
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.
Many-body localization in periodically driven systems.
Ponte, Pedro; PapiÄ‡, Z; Huveneers, FranÃ§ois; 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)Â 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)Â 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
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.
Rotation of Quantum Impurities in the Presence of a Many-Body Environment.
Schmidt, Richard; Lemeshko, Mikhail
2015-05-22
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. PMID:26047225
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.
Engineering many-body quantum dynamics by disorder
NASA Astrophysics Data System (ADS)
Buonsante, Pierfrancesco; Wimberger, Sandro
2008-04-01
Going beyond the currently investigated regimes in experiments on quantum transport of ultracold atoms in disordered potentials, we predict a crossover between regular and quantum-chaotic dynamics when varying the strength of disorder. Our spectral approach is based on the Bose-Hubbard model describing interacting atoms in deep random potentials. The predicted crossover from localized to diffusive dynamics depends on the simultaneous presence of interactions and disorder and can be verified in the laboratory by monitoring the evolution of typical experimental initial states.
Relativistic effects in nuclear many-body systems
Coester, F.
1985-01-01
Different approaches to the formulation of relativistic many-body dynamics yield different perspectives of nature and the magnitude of ''relativistic effects''. The effects of Lorentz invariance appear to be relatively unimportant. Important dynamical features of spinorial many-body formalisms are effects of subnuclear degrees of freedom which are represented in the many-body forces of the covariant nuclear Hamiltonian. 24 refs.
Critical quasienergy states in driven many-body systems
NASA Astrophysics Data System (ADS)
Bastidas, V. M.; Engelhardt, G.; Pérez-Fernández, P.; Vogl, M.; Brandes, T.
2014-12-01
We discuss singularities in the spectrum of driven many-body spin systems. In contrast to undriven models, the driving allows us to control the geometry of the quasienergy landscape. As a consequence, one can engineer singularities in the density of quasienergy states by tuning an external control. We show that the density of levels exhibits logarithmic divergences at the saddle points, while jumps are due to local minima of the quasienergy landscape. We discuss the characteristic signatures of these divergences in observables such as the magnetization, which should be measurable with current technology.
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
Entanglement dynamics of many-body systems: Analytical results
NASA Astrophysics Data System (ADS)
de Paula, A. L.; de Oliveira, J. G. G.; de Faria, J. G. Peixoto; Freitas, Dagoberto S.; Nemes, M. C.
2014-02-01
We consider a many-body system consisting of a harmonic oscillator linearly coupled to N others and solve the corresponding dynamical problem analytically. Initially, the main oscillator is prepared in a superposition of two coherent states and the N others in the ground states. We divide this system in arbitrary three partitions and the entanglement dynamics between any of these partitions is quantified. We show that the residual entanglement of the tripartite system is always present. Besides, the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. Finally, we obtain a hierarchy of entanglement between the central oscillator and partitions formed by the other oscillators. For long times the excitations of the main oscillator are completely transferred to the N others and these are found entangled.
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.
Low-frequency conductivity in many-body localized systems
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Sarang; Müller, Markus; Khemani, Vedika; Knap, Michael; Demler, Eugene; Huse, David A.
2015-09-01
We argue that the ac conductivity ? (? ) in the many-body localized phase is a power law of frequency ? at low frequency: specifically, ? (? ) ˜?? with the exponent ? approaching 1 at the phase transition to the thermal phase, and asymptoting to 2 deep in the localized phase. We identify two separate mechanisms giving rise to this power law: deep in the localized phase, the conductivity is dominated by rare resonant pairs of configurations; close to the transition, the dominant contributions are rare regions that are locally critical or in the thermal phase. We present numerical evidence supporting these claims, and discuss how these power laws can also be seen through polarization-decay measurements in ultracold atomic systems.
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.
Spectral statistics of chaotic many-body systems
NASA Astrophysics Data System (ADS)
Dubertrand, RÃ©my; MÃ¼ller, 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 SchrÃ¶dinger (or Grossâ€“Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Boseâ€“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 SchrÃ¶dinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wignerâ€“Dyson ensembles of random matrix theory. The conditions for Wignerâ€“Dyson statistics involve a gap in the spectrum of the Frobeniusâ€“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.
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.
Quantum Simulation with Circuit-QED Lattices: from Elementary Building Blocks to Many-Body Theory
NASA Astrophysics Data System (ADS)
Zhu, Guanyu
Recent experimental and theoretical progress in superconducting circuits and circuit QED (quantum electrodynamics) has helped to develop high-precision techniques to control, manipulate, and detect individual mesoscopic quantum systems. A promising direction is hence to scale up from individual building blocks to form larger-scale quantum many-body systems. Although realizing a scalable fault-tolerant quantum computer still faces major barriers of decoherence and quantum error correction, it is feasible to realize scalable quantum simulators with state-of-the-art technology. From the technological point of view, this could serve as an intermediate stage towards the final goal of a large-scale quantum computer, and could help accumulating experience with the control of quantum systems with a large number of degrees of freedom. From the physical point of view, this opens up a new regime where condensed matter systems can be simulated and studied, here in the context of strongly correlated photons and two-level systems. In this thesis, we mainly focus on two aspects of circuit-QED based quantum simulation. First, we discuss the elementary building blocks of the quantum simulator, in particular a fluxonium circuit coupled to a superconducting resonator. We show the interesting properties of the fluxonium circuit as a qubit, including the unusual structure of its charge matrix elements. We also employ perturbation theory to derive the effective Hamiltonian of the coupled system in the dispersive regime, where qubit and the photon frequencies are detuned. The observables predicted with our theory, including dispersive shifts and Kerr nonlinearity, are compared with data from experiments, such as homodyne transmission and two-tone spectroscopy. These studies also relate to the problem of detection in a circuit-QED quantum simulator. Second, we study many-body physics of circuit-QED lattices, serving as quantum simulators. In particular, we focus on two different directions which complement each other. One is concerned with quantum phases, such as photon pairing states, arising from the specific nature of light-matter interaction not usually encountered in conventional condensed matter materials. The second deals with interacting photons in a very specific lattice, the Kagome lattice. In that case, interesting liquid-crystal-like quantum phases, such as a nematic superfluid and a Wigner crystal, arise from the geometric frustration of the lattice.
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.
How an interacting many-body system tunnels through a potential barrier to open space
Lode, Axel U.J.; Streltsov, Alexej I.; Sakmann, Kaspar; Alon, Ofir E.; Cederbaum, Lorenz S.
2012-01-01
The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of ?-decay, fusion and fission in nuclear physics, and photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constituent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a transparent and controllable physical system, an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schrödinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: The overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wave function in the respective processes. PMID:22869703
Two-band Bose-Hubbard model for many-body resonant tunneling in the Wannier-Stark system
NASA Astrophysics Data System (ADS)
Parra-Murillo, Carlos A.; Madroñero, Javier; Wimberger, Sandro
2013-09-01
We study an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A crossover between regular and quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the nonequilibrium dynamics of our many-body system in different parameter regimes.
Entanglement and dynamics in many-body systems
NASA Astrophysics Data System (ADS)
Chandran, Anushya
In the first part of this dissertation, we study the dynamics of isolated and clean quantum systems out of equilibrium. We initially address the Kibble-Zurek (KZ) problem of determining the dynamical evolution of a system close to its critical point under slow changes of a control parameter. We formulate a scaling limit in which the nonequilibrium behavior is universal and discuss the universal content. We then report computations of some scaling functions in model Gaussian and large-N problems. Next, we apply KZ scaling to topologically ordered systems with no local order parameter. In the examples of the Ising gauge theory and the SU(2)k phases of the Levin-Wen models, we observe a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase at late times for ramps across transitions that reduce topological order. We conclude by studying quenches in the quantum O(N) model in the infinite N limit in varying spatial dimensions. Despite the failure to equilibrate owing to an infinite number of emergent conservation laws, the qualitative features of late time states following quenches is predicted by the equilibrium phase diagram. In the second part of this dissertation, we explore the relationship between entanglement and topological order in fractional quantum Hall (FQH) phases. In 2008, Li and Haldane conjectured that the entanglement spectrum (ES), a presentation of the Schmidt values of a real space cut, reflects the energy spectrum of the FQH chiral edge. Specifically, both spectra should have the same quasi-degeneracy of eigenvalues everywhere in the phase. We offer an analytic, microscopic proof of this conjecture in the Read-Rezayi sequence of model states. We further identify a different ES that reflects the bulk quasihole spectrum and prove a bulk-edge correspondence in the ES. Finally, we show that the finite-size corrections of the ES of the Laughlin states reveal the fractionalization of the underlying quasiparticles.
Many-Body Effects and Lineshape of Intersubband Transitions in Semiconductor Quantum Wells
NASA Technical Reports Server (NTRS)
Ning, Cun-Zheng
2003-01-01
Intersubband Transition (ISBT) infrared (IR) absorption and PL in InAs/AlSb were studied for narrow Quantum Wells (QWs). A large redshift was observed (7-10 meV) as temperature increased. A comprehensive many-body theory was developed for ISBTs including contributions of c-c and c-phonon scatterings. Many-body effects were studied systematically for ISBTs. Redshift and linewidth dependence on temperature, as well as spectral features were well explained by theory.
Degeneracy of Many-Body Quantum States in an Optical Lattice under a Uniform Magnetic Field
Zhang Jian; Jian Chaoming; Zhai Hui; Ye Fei
2010-10-08
We prove a theorem that shows the degeneracy of many-body states for particles in a periodic lattice and under a uniform magnetic field depends on the total particle number and the flux filling ratio. Noninteracting fermions and weakly interacting bosons are given as two examples. For the latter case, the phenomenon can also be physically understood in terms of destructive quantum interference of multiple symmetry-related tunneling paths between classical energy minima, which is reminiscent of the spin-parity effect discovered in magnetic molecular clusters. We also show that the quantum ground state of a mesoscopic number of bosons in this system is not a simple mean-field state but a fragmented state even for very weak interactions.
Quantum Dynamics of Many-body Spin Chains Using Atomic Ions
NASA Astrophysics Data System (ADS)
Senko, Crystal
2014-05-01
Quantum simulation, a field in which well-controlled quantum systems are used to study many-body physics that would otherwise be challenging to model, has undergone a great deal of progress in recent years. In particular, trapped ions have proven an excellent platform for simulating quantum magnetism, with their long-lived coherence times, tunable spin-spin interactions mediated by optical dipole forces, and ease of individual readout. The manipulation of more than 10 spins is now routine and has allowed the study of dynamics that will be difficult to simulate classically in larger systems, such as spectroscopy of excitation energies (arXiv:1401.5751) and the spread of spin correlations in a system with long-range interactions (arXiv:1401.5088). In the near future, we expect to apply these techniques to the study of a variety of phenomena such as prethermalization in an isolated quantum system, and to upgrade the apparatus so as to handle many tens of spins, a system size well beyond what is classically calculable. 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.
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 SchrÃ¶dinger 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.
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.; Nikoli?, 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)
JuliÃ¡-DÃaz, Bruno; GraÃŸ, 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.
Quantum gases. Observation of many-body dynamics in long-range tunneling after a quantum quench.
Meinert, Florian; Mark, Manfred J; Kirilov, Emil; Lauber, Katharina; Weinmann, Philipp; Gröbner, Michael; Daley, Andrew J; Nägerl, Hanns-Christoph
2014-06-13
Quantum tunneling is at the heart of many low-temperature phenomena. In strongly correlated lattice systems, tunneling is responsible for inducing effective interactions, and long-range tunneling substantially alters many-body properties in and out of equilibrium. We observe resonantly enhanced long-range quantum tunneling in one-dimensional Mott-insulating Hubbard chains that are suddenly quenched into a tilted configuration. Higher-order tunneling processes over up to five lattice sites are observed as resonances in the number of doubly occupied sites when the tilt per site is tuned to integer fractions of the Mott gap. This forms a basis for a controlled study of many-body dynamics driven by higher-order tunneling and demonstrates that when some degrees of freedom are frozen out, phenomena that are driven by small-amplitude tunneling terms can still be observed. PMID:24926015
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)).
Quantum simulation of many-body physics with neutral atoms, molecules, and ions
NASA Astrophysics Data System (ADS)
Foss-Feig, Michael
2013-05-01
The achievement of quantum degeneracy in alkali vapors has enabled the simulation of iconic condensed-matter models. However, ultracold alkali atoms are not yet cold enough to simulate the most interesting and poorly understood low-temperature properties of those models. In this talk, I will emphasize how the rich internal structure of alkaline earth atoms, ions, and molecules can be leveraged to simulate complex many-body physics in presently accessible experimental settings. I will begin by examining how alkaline earth atoms can be used to simulate the physics of so-called heavy fermion materials, and will show how the exotic groundstate properties of those materials manifests in non-equilibrium dynamics at relatively warm temperatures. Not surprisingly, the rich structure of alkaline earth atoms and molecules comes with a price, in many cases increasing the susceptibility of these systems to decoherence. A particularly troubling feature common to alkaline earth atoms and many molecules is the possibility of two-body loss. However, I will show that such loss can be harnessed to drive optically excited alkaline earth atoms and reactive molecules into highly-entangled non-equilibrium steady states, which could be used in the near future to improve the accuracy of high precision atomic clocks operated with alkaline earth atoms. The fate of interacting quantum systems in the presence of decoherence is of interest much more broadly, and I will conclude by describing how trapped ion systems provide a natural platform for addressing this issue. In particular, I will describe an exact solution of the dissipative Ising models that govern trapped ion systems, which affords both a qualitative and quantitative understanding of the effects of decoherence on these large-scale quantum simulators.
Many-body force and mobility measurements in colloidal systems
NASA Astrophysics Data System (ADS)
Merrill, Jason W.
We have extended a sensitive probe of colloidal interparticle forces, blinking optical tweezers, to allow measurements of forces among groups of more than two particles. This dissertation focuses on bridging the gap between microscopic pair interactions and bulk behavior in colloidal systems by using this technique to explore the regime of few-body interactions between micron-size polymer beads suspended in oil. Electrostatic forces and each component of the mobility tensor of small groups of colloidal particles are simultaneously measured using blinking optical tweezers. When the electrostatic screening length is longer than the inter-particle separation, forces are found to be non-pairwise additive. Both pair and multi-particle forces are well described by the linearized Poisson-Boltzmann equation with constant potential boundary conditions. These findings may play an important role in understanding the structure and stability of a wide variety of systems, from micron-sized particles in oil to aqueous nanocolloids. The measurement technique presented here should be simple to further extend to systems of heterogeneous, non-spherical particles arranged in arbitrary three dimensional geometries.
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.
Quantum simulation of many-body physics with neutral atoms, molecules, and ions
NASA Astrophysics Data System (ADS)
Foss-Feig, Michael
Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task. In this thesis, we emphasize how the unique features of particular atomic and molecular systems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline-earth atoms. In particular, we show how groundstate properties—for instance anomalous mass enhancement—can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.
Exact numerical methods for a many-body Wannier-Stark system
NASA Astrophysics Data System (ADS)
Parra-Murillo, Carlos A.; Madroñero, Javier; Wimberger, Sandro
2015-01-01
We present exact methods for the numerical integration of the Wannier-Stark system in a many-body scenario including two Bloch bands. Our ab initio approaches allow for the treatment of a few-body problem with bosonic statistics and strong interparticle interaction. The numerical implementation is based on the Lanczos algorithm for the diagonalization of large, but sparse symmetric Floquet matrices. We analyze the scheme efficiency in terms of the computational time, which is shown to scale polynomially with the size of the system. The numerically computed eigensystem is applied to the analysis of the Floquet Hamiltonian describing our problem. We show that this allows, for instance, for the efficient detection and characterization of avoided crossings and their statistical analysis. We finally compare the efficiency of our Lanczos diagonalization for computing the temporal evolution of our many-body system with an explicit fourth order Runge-Kutta integration. Both implementations heavily exploit efficient matrix-vector multiplication schemes. Our results should permit an extrapolation of the applicability of exact methods to increasing sizes of generic many-body quantum problems with bosonic statistics.
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.
Hybrid quantum magnetism in circuit QED: from spin-photon waves to many-body spectroscopy.
Kurcz, Andreas; Bermudez, Alejandro; García-Ripoll, Juan José
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
Cavity quantum electrodynamics with many-body states of a two-dimensional electron gas.
Smolka, Stephan; Wuester, Wolf; Haupt, Florian; Faelt, Stefan; Wegscheider, Werner; Imamoglu, AtaÃ§
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
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.
Single-particle and many-body analyses of a quasiperiodic integrable system after a quench
NASA Astrophysics Data System (ADS)
He, Kai; Santos, Lea F.; Wright, Tod M.; Rigol, Marcos
2013-06-01
In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-André model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.
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 fluctuationsâ€”a critical accuracy threshold highly coveted during molecular simulationsâ€”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
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.
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.
Renormalization of myoglobin-ligand binding energetics by quantum many-body effects.
Weber, Cédric; Cole, Daniel J; O'Regan, David D; Payne, Mike C
2014-04-22
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
Renormalization of myoglobinâ€“ligand binding energetics by quantum many-body effects
Weber, CÃ©dric; Cole, Daniel J.; Oâ€™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 Feâ€“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 Hundâ€™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.
Quantum many-body effects on the electric and thermoelectric response of molecular heterojunctions
NASA Astrophysics Data System (ADS)
Bergfield, Justin; Stafford, Charles
2009-03-01
A semi-empirical ?-electron Hamiltonian (extended Hubbard model) is used to model the electronic degrees of freedom most relevant for transport in a heterojunction consisting of a conjugated organic molecule coupled to two (or more) metallic electrodes. With an appropriate choice of parameters, the complete spectrum of electronic excitations of the molecule up to 8--10eV can be accurately described,^1 which is essential to accurately model transport far from equilibrium. The electric and thermoelectric response of the junction is calculated within a many-body theory of transport based on nonequilibrium Green's functions. For benzenedithiol-Au junctions, the parameters characterizing the lead-molecule coupling (tunneling width and chemical potential offset) are determined by comparison to linear-response measurements of conductance and thermopower. The nonlinear transport can then be predicted: the differential conductance as a function of gate and bias voltages exhibits clear signatures of charge quantization and resonant tunneling through excited states, with an irregular ``molecular diamond'' structure analogous to the regular Coulomb diamonds observed in quantum dot transport experiments. Several other small conjugated organic molecules are also investigated. ^1C. W. M. Castelton and W. Barford, J. Chem. Phys. 117, 3570 (2002).
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.
NASA Astrophysics Data System (ADS)
Zangara, Pablo R.; Bendersky, Denise; Pastawski, Horacio M.
2015-04-01
We address the question of how weak perturbations, which are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid-state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by nonreversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed N spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as N increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems
NASA Astrophysics Data System (ADS)
Salerno, Mario; Popkov, Vladislav
2010-07-01
Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n?1 . As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T . The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T?Tc , is demonstrated.
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.
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 â€œfragmentation levelâ€ (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 â€œvirial coefficientâ€ 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.: 30â€‰053 No. of bytes in distributed program, including test data, etc.: 801â€‰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, â€œfragmentation levelâ€, â€œaverage system radiusâ€, â€œvirial coefficientâ€, and energy conservation precision test. Additional comments: Easy copy/paste based deployment method. Running time: Quadratic complexity.
NASA Astrophysics Data System (ADS)
Jones, Andrew P.; Crain, Jason; Sokhan, Vlad P.; Whitfield, Troy W.; Martyna, Glenn J.
2013-04-01
Treating both many-body polarization and dispersion interactions is now recognized as a key element in achieving the level of atomistic modeling required to reveal novel physics in complex systems. The quantum Drude oscillator (QDO), a Gaussian-based, coarse grained electronic structure model, captures both many-body polarization and dispersion and has linear scale computational complexity with system size, hence it is a leading candidate next-generation simulation method. Here, we investigate the extent to which the QDO treatment reproduces the desired long-range atomic and molecular properties. We present closed form expressions for leading order polarizabilities and dispersion coefficients and derive invariant (parameter-free) scaling relationships among multipole polarizability and many-body dispersion coefficients that arise due to the Gaussian nature of the model. We show that these “combining rules” hold to within a few percent for noble gas atoms, alkali metals, and simple (first-row hydride) molecules such as water; this is consistent with the surprising success that models with underlying Gaussian statistics often exhibit in physics. We present a diagrammatic Jastrow-type perturbation theory tailored to the QDO model that serves to illustrate the rich types of responses that the QDO approach engenders. QDO models for neon, argon, krypton, and xenon, designed to reproduce gas phase properties, are constructed and their condensed phase properties explored via linear scale diffusion Monte Carlo (DMC) and path integral molecular dynamics (PIMD) simulations. Good agreement with experimental data for structure, cohesive energy, and bulk modulus is found, demonstrating a degree of transferability that cannot be achieved using current empirical models or fully ab initio descriptions.
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.
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 PoincarÃ© (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 Î±-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 Î±-cluster correlation becomes particularly important at lower density, such as in the excited states of some nuclei (e.g., the Î±-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 MusÃ©e 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
Hermann, Andreas; Krawczyk, Robert P.; Lein, Matthias; Schwerdtfeger, Peter; Hamilton, I. P.; Stewart, James J. P.
2007-07-15
The many-body expansion of the interaction potential between atoms and molecules is analyzed in detail for different types of interactions involving up to seven atoms. Elementary clusters of Ar, Na, Si, and, in particular, Au are studied, using first-principles wave-function- and density-functional-based methods to obtain the individual n-body contributions to the interaction energies. With increasing atom number the many-body expansion converges rapidly only for long-range weak interactions. Large oscillatory behavior is observed for other types of interactions. This is consistent with the fact that Au clusters up to a certain size prefer planar structures over the more compact three-dimensional Lennard-Jones-type structures. Several Au model potentials and semiempirical PM6 theory are investigated for their ability to reproduce the quantum results. We further investigate small water clusters as prototypes of hydrogen-bonded systems. Here, the many-body expansion converges rapidly, reflecting the localized nature of the hydrogen bond and justifying the use of two-body potentials to describe water-water interactions. The question of whether electron correlation contributions can be successfully modeled by a many-body interaction potential is also addressed.
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 ? 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. Additiona
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 system–detector 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 Mach–Zehnder 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 system–detector interaction strength. These oscillations are a genuine many-body effect, and can be experimentally observed through the voltage dependence of cross current correlations.
Stability and Clustering for Lattice Many-Body Quantum Hamiltonians with Multiparticle Potentials
NASA Astrophysics Data System (ADS)
Faria da Veiga, Paulo A.; O'Carroll, Michael
2015-11-01
We analyze a quantum system of N identical spinless particles of mass m, in the lattice Z^d, given by a Hamiltonian H_N=T_N+V_N, with kinetic energy T_N? 0 and potential V_N=V_{N,2}+V_{N,3} composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials V_{N,2} and V_{N,3} on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the H_N spectrum, \\underline{? }(H_N)? -cN, for c>0 independent of N. For V_{N,3}=0, H_N is unstable, and the system collapses. If V_{N,3}not =0, H_N is stable and, for strong enough repulsion, we obtain \\underline{? }(H_N)? -c' N, where c'N is the energy of ( N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [ \\underline{? }(V_N)/N ] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value N_s of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers N_r and N_s-N_r, with N_r=1,ldots ,N_s-1.
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.
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.
Quantum Optical Lattices for Emergent Many-Body Phases of Ultracold Atoms.
Caballero-Benitez, Santiago F; Mekhov, Igor B
2015-12-11
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. PMID:26705634
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, 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}.
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.
A driven similarity renormalization group approach to quantum many-body problems.
Evangelista, Francesco A
2014-08-01
Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. G?azek 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. PMID:25106572
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. GÅ‚azek 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.
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 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. 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.
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 Î± <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 Ëœlog 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 /Î¾ , where L is the length of the system and Î¾ is the correlation length, which has a power-law divergence at the critical point.
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 ?m 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
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.
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 (Fermiâ€“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.
Many-body dispersion corrections for periodic systems: an efficient reciprocal space implementation
NASA Astrophysics Data System (ADS)
Bu?ko, 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.
Paradoxical probabilistic behavior for strongly correlated many-body classical systems
NASA Astrophysics Data System (ADS)
Jauregui, Max; Tsallis, Constantino
2015-09-01
Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that each row is a list of n strongly correlated random variables. The correlations are preserved even when n ? ?, since the standard central limit theorem does not hold for this array. We show that, if we choose a fixed number m < n of random variables of the nth row and trace over the other n - m variables, and then consider n ? ?, the m chosen ones can, paradoxically, turn out to be independent. However, the scenario can be different if m increases with n. Finally, we suggest a possible experimental verification of our results near criticality of a second-order phase transition.
Many-body dispersion corrections for periodic systems: an efficient reciprocal space implementation.
Bu?ko, 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. PMID:26753609
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 effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid theory
NASA Astrophysics Data System (ADS)
Arakawa, Naoya
2015-06-01
I review many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point (QCP). These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multi-orbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multi-orbital systems. To improve this situation, I formulate the resistivity of a multi-orbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki-Thompson term. The results away from and near the antiferromagnetic QCP reproduce the temperature dependence observed in Sr2RuO4 and Sr2Ru0.075Ti0.025O4, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.
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
Krishnamoorthy, Sriram; Bernholdt, David E; Pitzer, R. M.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
Hartono, Albert; Lu, Qingda; henretty, thomas; Krishnamoorthy, Sriram; zhang, huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-11-12
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.
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; Belof, Jonathan L; Space, Brian
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. PMID:24320259
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)
Papi?, 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)
GutiÃ©rrez, 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 excitationsâ€”often referred to as the blockade radiusâ€”is not a static but rather a dynamic quantity.
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.
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.
Understanding the many-body expansion for large systems. I. Precision considerations.
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?O)??. 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. PMID:25005278
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 â©¾ 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 studymoreÂ Â» 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.Â«Â less
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.
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
NASA Astrophysics Data System (ADS)
Abbaspour, Mohsen
2012-01-01
The Fowler's expression for calculation of the reduced surface tension and surface energy has been used with Lennard-Jones (LJ) and two-body Hartree-Fock dispersion (HFD)-like potentials for neon and argon, respectively. The required radial distribution functions (RDFs) have been used from two recently determined expressions in the literature and a new equation proposed in this work. Quantum corrections for neon system have been considered using the Feynman-Hibbs (FH) and Wigner-Kirkwood (WK) approaches. To take many-body forces into account for argon system, the simple three-body potentials of Wang and Sadus (2006) [33] and Hauschild and Prausnitz (1993) [30] used with the HFD-like potential without requiring an expensive three-body calculation. The results show that the quantum and three-body effects improve the prediction of the surface tension of liquid neon and argon using the Fowler's expression.
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)
Å amaj, Ladislav Ã….; Bajnok, ZoltÃ¡n
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.
NASA Astrophysics Data System (ADS)
Barmettler, Peter; Punk, Matthias; Gritsev, Vladimir; Demler, Eugene; Altman, Ehud
2010-05-01
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.
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
Double decimation and sliding vacua in the nuclear many-body system
NASA Astrophysics Data System (ADS)
Brown, G. E.; Rho, Mannque
2004-06-01
We propose that effective field theories for nuclei and nuclear matter comprise of “double decimation”: (1) the chiral symmetry decimation (CSD) and (2) Fermi liquid decimation (FLD). The Brown-Rho scaling recently identified as the parametric dependence intrinsic in the “vector manifestation” of hidden local symmetry theory of Harada and Yamawaki results from the first decimation. This scaling governs dynamics down to the scale at which the Fermi surface is formed as a quantum critical phenomenon. The next decimation to the top of the Fermi sea where standard nuclear physics is operative makes up the FLD. Thus, nuclear dynamics are dictated by two fixed points, namely, the vector manifestation fixed point and the Fermi liquid fixed point. It has been a prevalent practice in nuclear physics community to proceed with the second decimation only, assuming density-independent masses, without implementing the first, CSD. We show why most nuclear phenomena can be reproduced by theories using either density-independent, or density-dependent masses, a grand conspiracy of nature that is an aspect that could be tied to the Cheshire Cat phenomenon in hadron physics. We identify what is left out in the FLD that does not incorporate the CSD. Experiments such as the dilepton production in relativistic heavy ion reactions, which are specifically designed to observe effects of dropping masses, could exhibit large effects from the reduced masses. However, they are compounded with effects that are not directly tied to chiral symmetry. We discuss a recent STAR/RHIC observation where BR scaling can be singled out in a pristine environment.
(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.
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.
Anomalous decoherence and absence of thermalization in a photonic many-body system
NASA Astrophysics Data System (ADS)
Larson, Jonas
2011-05-01
The intention of this work is twofold: first, to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons and, second, to study various outcomes deriving from inherent or external decoherence. A qubit induces an effective coupling between two externally pumped cavity modes. Without cavity losses and in the dispersive regime, intrinsic Josephson oscillations of photons between the two modes occurs. In this case, contrary to regular Markovian decoherence, the qubit purity shows a Gaussian decay and recurrence of its coherence. Due to intrinsic nonlinearities, both the Josephson oscillations as well as the qubit properties display a rich collapse-revival structure, where, however, the complexity of the qubit evolution is in some sense stronger. The qubit as a meter of the photon dynamics is considered, and it is shown that qubit dephasing, originating, for example, from nondemolition measurements, results in an exponential destruction of the oscillations which manifests the collectiveness of the Josephson effect. Nonselective qubit measurements, on the other hand, render a Zeno effect seen in a slowing down of the Josephson oscillations. Contrary to dephasing, cavity dissipation results in a Gaussian decay of the scaled Josephson oscillations. Finally, following Ponomarev [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.010405 106, 010405 (2011)], we analyze aspects of thermalization. In particular, despite similarities with the generic model studied by Ponomarev , our system does not seem to thermalize.
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.
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.
Ab initio calculation of d-metal L-edge RIXS spectra using many-body quantum chemistry methods
NASA Astrophysics Data System (ADS)
Bogdanov, Nikolay; Bisogni, Valentina; Geck, Jochen; Hozoi, Liviu; van den Brink, Jeroen
2014-03-01
We designed a fully ab initio quantum chemistry scheme for the computation of both d-d excitation energies and intensities as measured by resonant inelastic x-ray scattering (RIXS) in d-electron systems. RIXS has recently emerged as a powerful tool to reliably probe the charge, spin, and orbital degrees of freedom of correlated electrons in solids. As a first application we picked up Li2CuO2, a quasi-1D Cu 3d9 oxide with a simple valence configuration in the intermediate state. We use embedded-cluster MCSCF and MRCI techniques, including scalar relativistic effects, spin-orbit coupling, and the valence orbital relaxation in the presence of the core hole. The transition matrix elements of the dipole operator are obtained by non-orthogonal configuration interaction. A careful analysis of the RIXS spectra is important for understanding the interplay between local distortions and longer-range lattice anisotropy and its effect on the d-level electronic structure and magnetic interactions.
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 Î´ 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; AlfÃ¨, 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 Â± 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
Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, 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.
D?ugosz, Maciej; Antosiewicz, Jan M
2015-07-01
Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies. PMID:26068580
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ?slant n ?slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
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.
NASA Astrophysics Data System (ADS)
MacDonald, Allan H.
2014-03-01
Most current electronic devices use gate voltages to switch individual electron transport channels or off. This architecture necessarily leads to operating voltages that are much larger than the temperature thermal energy, and places lower bounds on power consumption that are becoming. I will discuss strategies for achieving devices in which gates are used to collective many-electron states, in principle allowing charge transport to be switched by smaller voltage changes and both operating voltages and power consumption to reduced. I will specifically address devices based on the properties of itinerant electroninsulating magnetic systems, and devices based on bilayer exciton condensation. This work is based on work performed in collaboration with Sanjay Banerjee and Frank Register.
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.
Georgescu, Ionu? 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.
Many-Body Physics, Topology and Geometry
NASA Astrophysics Data System (ADS)
Sen, Siddhartha; Gupta, Kumar Sankar
2015-06-01
The challenge of condensed matter physics is to use non relativistic quantum ideas to explain and predict the observed oscopic properties of matter. To do this great ingenuity and imagination is required. The Hamiltonian H of a many-body system can be written down schematically as
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.
Efficient interacting many body similations using GPUs
NASA Astrophysics Data System (ADS)
Kramer, Tobias
2012-02-01
Graphics Processing Units (GPUs) provide an ideal tool to study interacting systems using classical machanics with huge speedups for example in molecular dynamics. The quantum-mechanical calculations of many-body systems require additional work, but are feasible using additional degrees of freedom to incorporate quantum-mechanical effects [1]. As an example of the method I show the self-consistent solution to the current transport in a magnetic field can be obtained from a microscopic model with thousands of Coulomb interacting electrons. This yields a microscopic model of the Hall effect [2]. For few electron systems I compare the electronic density evolution based on the GPU classical-quantum model to TD-DFT calculations and discuss prospects of GPUs for solving the Schrodinger equation for many-particles. [4pt] [1] Time dependent approach to transport and scattering in atomic and mesoscopic systems, T. Kramer AIP Conf. Proc., 1334, 142 (2011) [0pt] [2] Self-consistent calculation of electric potentials in Hall devices, T. Kramer, V. Krueckl, E. Heller, and R. Parrott Phys. Rev. B, 81, 205306 (2010)
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)
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)
Hernandez-Quiroz, Saul; Benet, Luis
2010-03-15
We study the nearest-neighbor distributions of the k-body embedded ensembles of random matrices for n bosons distributed over two-degenerate single-particle states. This ensemble, as a function of k, displays a transition from harmonic-oscillator behavior (k=1) to random-matrix-type behavior (k=n). We show that a large and robust quasidegeneracy is present for a wide interval of values of k when the ensemble is time-reversal invariant. These quasidegenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of k and discuss the statistical properties of the splittings of these doublets.
Atomistic simulations of stainless steels: a many-body potential for the Fe-Cr-C system
NASA Astrophysics Data System (ADS)
Henriksson, K. O. E.; Björkas, C.; Nordlund, K.
2013-11-01
Stainless steels found in real-world applications usually have some C content in the base Fe-Cr alloy, resulting in hard and dislocation-pinning carbides—Fe3C (cementite) and Cr23C6—being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe-Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell-Brenner-Tersoff form for the entire Fe-Cr-C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe-Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe-Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe.
Many-Body van der Waals Effects in Advanced Materials
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre; von Lilienfeld, Anatole; Distasio, Robert A., Jr.
2013-03-01
Van der Waals (vdW) interactions are ubiquitous in molecules and condensed matter. These interactions are inherently quantum mechanical phenomena that arise from concerted correlations between many electrons within a given molecular system. Despite this fact, the vast majority of theoretical calculations include long-range vdW interactions based on a simple effective interatomic pairwise model. We introduce an efficient method that accurately describes the full long-range many-body vdW energy, and demonstrate that many-body contributions can significantly exceed the highly coveted ``chemical accuracy''. Cases studied include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes. Our findings suggest that inclusion of the many-body vdW energy is essential for achieving chemical accuracy and therefore must be accounted for when studying advanced materials.
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.
Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
NASA Astrophysics Data System (ADS)
Brauner, Tomáš; Moroz, Sergej
2014-12-01
We classify effective actions for Nambu-Goldstone (NG) bosons assuming the absence of anomalies. Special attention is paid to Lagrangians that are invariant only up to a surface term, which are shown to be in a one-to-one correspondence with Chern-Simons (CS) theories for unbroken symmetry. Without making specific assumptions on the spacetime symmetry, we give explicit expressions for these Lagrangians, generalizing the Berry and Hopf terms in ferromagnets. Globally well-defined matrix expressions are derived for symmetric coset spaces of broken symmetry. The CS Lagrangians exhibit special properties, on both the perturbative and the global topological levels. The order-one CS term is responsible for the noninvariance of the canonical momentum density under internal symmetry, known as the linear momentum problem. The order-three CS term gives rise to a novel type of interaction among NG bosons. All the CS terms are robust against local variations of microscopic physics.
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.
Ogawa, Y.; Minami, F.
2013-12-04
We show the coherent control of dephasing process of exciton polarization due to heavy hole-heavy hole and heavy hole-light hole scatterings in a GaAs single quantum well. The memory time of the exction scattering is estimated as 0.47 ps.
Sliusarenko, O. Yu.; Chechkin, A. V.; Slyusarenko, Yu. V.
2015-04-15
By generalizing Bogolyubovâ€™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 Hamiltonâ€™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.
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.
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.
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.
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.
Emergence of stationary many-body entanglement in driven-dissipative Rydberg lattice gases
NASA Astrophysics Data System (ADS)
Lee, Sun Kyung; Cho, Jaeyoon; Choi, K. S.
2015-11-01
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to examine driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary locally reduce the entropy of the many-body system. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady state, precisely as with optical pumping. We characterize the dynamics of multipartite entanglement in an one-dimensional lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.
Interferometric probes of many-body localization.
Serbyn, M; Knap, M; Gopalakrishnan, S; PapiÄ‡, 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.
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.
Dynamical stability of a many-body Kapitza pendulum
Citro, Roberta; Dalla Torre, Emanuele G.; Dâ€™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 sineâ€“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.
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.
Many body theory of stochastic gene expression
NASA Astrophysics Data System (ADS)
Walczak, Aleksandra M.
The regulation of expression states of genes in cells is a stochastic process. The relatively small numbers of protein molecules of a given type present in the cell and the nonlinear nature of chemical reactions result in behaviours, which are hard to anticipate without an appropriate mathematical development. In this dissertation, I develop theoretical approaches based on methods of statistical physics and many-body theory, in which protein and operator state dynamics are treated stochastically and on an equal footing. This development allows me to study the general principles of how noise arising on different levels of the regulatory system affects the complex collective characteristics of systems observed experimentally. I discuss simple models and approximations, which allow for, at least some, analytical progress in these problems. These have allowed us to understand how the operator state fluctuations may influence the steady state properties and lifetimes of attractors of simple gene systems. I show, that for fast binding and unbinding from the DNA, the operator state may be taken to be in equilibrium for highly cooperative binding, when predicting steady state properties as is traditionally done. Nevertheless, if proteins are produced in bursts, the DNA binding state fluctuations must be taken into account explicitly. Furthermore, even when the steady state probability distributions are weakly influenced by the operator state fluctuations, the escape rate in biologically relevant regimes strongly depends on transcription factor-DNA binding rates.
Local conservation laws and the structure of the many-body localized states.
Serbyn, Maksym; Papi?, 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
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.
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.
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.
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; MÃ¼ller, 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.
Amusia, M.Ya. |
1995-01-01
The author presents this article in the volume, dedicated to the 70th birthday of Academician S. T. Belyaev. He has known him personally since 1961 and admires his profound contributions to the theory of Bose-liquids, to the theory of superconductivity of atomic nuclei and some other important scientific works. Belyaev is well known also as an organizer of science and education. For years he was, and is still the Chairman of the Synchrotron Radiation Commission of the Russian Academy of Science, a body which was established long ago to promote construction of high intensity light sources, and technological as well as scientific research using this light. One of the important directions of this study is investigation of photoabsorbtion by multielectron atoms in order to obtain information about their structure.
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.
NASA Astrophysics Data System (ADS)
Zakharov, A. Yu.; Zakharov, M. A.
2016-01-01
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems.
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
Uncovering many-body correlations in nanoscale nuclear spin baths by central spin decoherence
NASA Astrophysics Data System (ADS)
Ma, Wen-Long; Wolfowicz, Gary; Zhao, Nan; Li, Shu-Shen; Morton, John J. L.; Liu, Ren-Bao
2014-09-01
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.
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
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 SchrÃ¶dinger 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 exchangeâ€“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 Fermiâ€“Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.
On the simulation of indistinguishable fermions in the many-body Wigner formalism
NASA Astrophysics Data System (ADS)
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.
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.
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.
Observation of coherent quench dynamics in a metallic many-body state of fermionic atoms.
Will, Sebastian; Iyer, Deepak; Rigol, Marcos
2015-01-01
Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter. So far, coherent nonequilibrium dynamics has exclusively been observed in ultracold many-body systems of bosonic atoms. Here we report on the observation of coherent quench dynamics of fermionic atoms. A metallic state of ultracold spin-polarized fermions is prepared along with a Bose-Einstein condensate in a shallow three-dimensional optical lattice. After a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons, we observe long-lived coherent oscillations in the fermionic momentum distribution, with a period that is determined solely by the Fermi-Bose interaction energy. Our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalized fermionic quantum states and for quantum metrology. PMID:25625799
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.
NASA Astrophysics Data System (ADS)
Wang, Jianhui
In this dissertation, we study the effects of the electron-electron Coulomb interaction in graphene. We first analyze the sublattice symmetric (i.e. density-density) and antisymmetric response functions and show that the latter has a singularity as a function of the coupling constant (which can be changed by changing the background dielectric constant) signalling the transition to the insulating phase. Furthermore, even for coupling constant smaller than the critical value, the effect of the Coulomb interaction is manifested in that the antisymmetric response function has a power law dependence on the momentum transfer and the exponent is a continuously varying function of the coupling constant. We also calculate the symmetric response for a model Hamiltonian numerically. The effects of the Coulomb interaction is also manifested as a correction to the excitation energy from a filled Landau level. We analyze the eigenvalue problem for magnetoexcitons in detail and compare the theory with experiments. Finally, we study how stable the high field quantum Hall states are against Landau level mixing, which is also an interaction effect, as the magnetic field is decreased.
Influence of many-body interactions during the ionization of gases by short intense optical pulses.
Schuh, K; Hader, J; Moloney, J V; Koch, S W
2014-03-01
The excitation of atomic gases by short high-intensity optical pulses leads to significant electron ionization. In dilute systems, the generated distribution of ionized electrons is highly anisotropic, reflecting the quantum mechanical properties of the atomic states involved in the many photon transitions. For higher atomic densities, the Coulomb interaction in the electron-ion system leads to the development of an isotropic electron plasma. To study the ionization process in the presence of the many-body interaction, a fully microscopic model is developed that combines a generalized version of the optical Bloch equations describing the optical excitation with a microscopic description of the many-body interactions. The numerical evaluation shows that the Coulomb interaction significantly modifies the distribution anisotropy already during the excitation process. Whereas a reduced anisotropy is still present after the pulse for low ionization degrees and pressures, it is completely absent for elevated gas densities. An ionization degree is predicted that is significantly enhanced by the many-body interactions. PMID:24730952
Many-body Landau-Zener tunneling in the Bose-Hubbard model
NASA Astrophysics Data System (ADS)
Tomadin, Andrea; Mannella, Riccardo; Wimberger, Sandro
2008-01-01
We study a model for ultracold, spinless atoms in quasi-one-dimensional optical lattices and subjected to a tunable tilting force. Statistical tests are employed to quantitatively characterize the spectrum of the Floquet-Bloch operator of the system along the transition from the regular to the quantum chaotic regime. Moreover, we perturbatively include the coupling of the one-band model to the second energy band. This allows us to study the Landau-Zener interband tunneling within a truly many-body description of ultracold atoms. The distributions of the computed tunneling rates provide an independent and experimentally accessible signature of the regular-chaotic transition.
Charge optimized many-body potential for aluminum
NASA Astrophysics Data System (ADS)
Choudhary, Kamal; Liang, Tao; Chernatynskiy, Aleksandr; Lu, Zizhe; Goyal, Anuj; Phillpot, Simon R.; Sinnott, Susan B.
2015-01-01
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 < {12\\bar{{1}}}> 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.
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 (1â€‰1â€‰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
Hong-Ou-Mandel Interference with Atomic Many-Body States
NASA Astrophysics Data System (ADS)
Islam, Rajibul; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Rispoli, Matthew; Tai, M. Eric; Greiner, Markus
2015-05-01
Hong-Ou-Mandel (HOM) interference experiments are a powerful probe for the indistinguishability and underlying quantum statistics of particles. In the classic HOM experiment, a pair of identical photons incident on different input ports of a beamsplitter exits via the same output port. Using the precise control and readout afforded by our quantum gas microscope, we present an implementation of this classic experiment using massive bosons in a doublewell optical potential. Identical states are prepared on each site of the doublewell and by lowering the tunnel coupling between the sites for specific times, we drive a beam splitter operation between the sites. For single-atom Fock input states, we have realized a high fidelity beamsplitter operation and observed an HOM interference contrast of >90%. By generalizing to more complex initial states on the input ports, we have been able to establish HOM experiment protocols as a robust approach towards studying the indistinguishability of many-body states as well as probe interaction-induced effects. These techniques open a path towards the measurement of purity in a quantum system and entanglement entropy in many-body states.
Fate of dynamical many-body localization in the presence of disorder
NASA Astrophysics Data System (ADS)
Roy, Analabha; Das, Arnab
2015-03-01
Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here we show that, although any randomness in the interactions of a many-body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale ? due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down (? shoots up) by orders of magnitude as the ratio of the drive frequency ? and amplitude h0 tends to certain specific values (the freezing condition). If ? is increased while maintaining the ratio h0/? at a fixed freezing value, then ? diverges exponentially with ? . The results can be easily extended for a larger family of disordered fermionic and bosonic systems.
Probing many-body localization by spin noise spectroscopy
NASA Astrophysics Data System (ADS)
Roy, Dibyendu; Singh, Rajeev; Moessner, Roderich
2015-11-01
We propose to apply spin noise spectroscopy (SNS) to detect many-body localization (MBL) in disordered spin systems. The SNS methods are relatively noninvasive techniques to probe spontaneous spin fluctuations. Here, we show that the spin noise signals obtained by cross-correlation SNS with two probe beams can be used to separate the MBL phase from a noninteracting Anderson localized phase and a delocalized (diffusive) phase in the studied models for which we numerically calculate real-time spin noise signals and their power spectra. For an archetypical case of the disordered XXZ spin chain, we also develop a simple phenomenological model.
Energy Level Alignment for Many-Body Resonant Tunneling
NASA Astrophysics Data System (ADS)
Walkenhorst, Jessica; Appel, Heiko; Helbig, Nicole; Rubio, Angel
2014-03-01
Electron tunneling plays a fundamental role in many chemical and physical processes, whilst electron tunneling at surfaces also attracts much attention due to its importance for charge transfer and carrier injection mechanisms e.g. in organic devices. Resonant tunneling is governed by the alignment of energy levels of donor and acceptor. While the separate systems are described well by standard approaches, the alignment of their chemical potentials is problematic since bringing donor and acceptor in contact changes the respective energy levels due to the electronic interaction. We investigate resonant many-body tunneling in a one dimensional donor-acceptor system, where the electrons interact via a softened Coulomb potential. For a system of few electrons, we solve the Schrödinger equation exactly. As first step we analyze the case of adiabatic tunneling. Starting from the description of tunneling between non-interacting systems, we derive the necessary energy correction terms for the case of the fully interacting donor-acceptor many-body system.
Many-body theory of electric and thermal transport in single-molecule heterojunctions
NASA Astrophysics Data System (ADS)
Bergfield, Justin
2010-03-01
Electron transport in single-molecule junctions (SMJ) is a key example of a strongly-correlated system far from equilibrium, with myriad potential applications in nanotechnology. When macroscopic leads are attached to a single molecule, a SMJ is formed, transforming the ``few-body'' molecular problem into a true ``many-body'' problem. Until recently, a theory of transport that properly accounts for both the particle and wave character of the electron has been lacking, so that the Coulomb blockade and coherent transport regimes were considered ``complementary.'' We have developed a nonequilibrium many-body theoryfootnotetextJ. P. Bergfield and C. A. Stafford, Phys. Rev. B 79, 245125 (2009). that reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously. Our approach is based on nonequilibrium Green's functions, enabling physically motivated approximations that sum terms to all orders. The junction Green's functions are calculated exactly in the sequential-tunneling limit, and the corrections to the electron self-energy due to finite tunneling width are included via Dyson-Keldysh equations. In this talk, I will present a brief overview of our many-body theory of SMJ and discuss the simulated linear and nonlinear response of a benzenedithiol-gold junction. I will also outline our derivation of an exact expression for the heat current in an interacting nanostructure, highlighting our predictionfootnotetextJ. P. Bergfield and C. A. Stafford, Nano Letters 9, 3072 (2009). of a dramatic quantum-induced enhancement of thermoelectric effects in the vicinity of a transmission node. Finally, I will provide several striking examples where the predictions of our many-body theory differ drastically from those of mean-field (density functional) theory.
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.
Constructing local integrals of motion in the many-body localized phase
NASA Astrophysics Data System (ADS)
Chandran, Anushya; Kim, Isaac H.; Vidal, Guifre; Abanin, Dmitry A.
2015-02-01
Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body-localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin-flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, in both experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin-chain model. We show that the resulting LIOMs are quasilocal and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.
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 â‰ˆ10 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.
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.
Elliptic Solutions to Difference Non-Linear Equations and Related Many-Body Problems
NASA Astrophysics Data System (ADS)
Krichever, I.; Wiegmann, P.; Zabrodin, A.
We study algebro-geometric (finite-gap) and elliptic solutions of fully discretized KP or 2D Toda equations. In bilinear form they are Hirota's difference equation for ?-functions. Starting from a given algebraic curve, we express the ?-function and the Baker-Akhiezer function in terms of the Riemann theta function. We show that the elliptic solutions, when the ?-function is an elliptic polynomial, form a subclass of the general algebro-geometric solutions. We construct the algebraic curves of the elliptic solutions. The evolution of zeros of the elliptic solutions is governed by the discrete time generalization of the Ruijsenaars-Schneider many body system. The zeros obey equations which have the form of nested Bethe-ansatz equations, known from integrable quantum field theories. We discuss the Lax representation and the action-angle-type variables for the many body system. We also discuss elliptic solutions to discrete analogues of KdV, sine-Gordon and 1D Toda equations and describe the loci of the zeros.
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 ) âˆt1 /z with a disorder-dependent exponent z â‰¥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 ) âˆt-Î¶ with a continuously varying disorder-dependent exponent Î¶ , 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
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 âˆ’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
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.
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. GrÃ¼neis 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 MÃ¸ller-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.
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 SchrÃ¶dinger 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).
Many-Body Dynamics of Dipolar Molecules in an Optical Lattice
NASA Astrophysics Data System (ADS)
Hazzard, Kaden R. A.; Gadway, Bryce; Foss-Feig, Michael; Yan, Bo; Moses, Steven A.; Covey, Jacob P.; Yao, Norman Y.; Lukin, Mikhail D.; Ye, Jun; Jin, Deborah S.; Rey, Ana Maria
2014-11-01
We use Ramsey spectroscopy to experimentally probe the quantum dynamics of disordered dipolar-interacting ultracold molecules in a partially filled optical lattice, and we compare the results to theory. We report the capability to control the dipolar interaction strength. We find excellent agreement between our measurements of the spin dynamics and theoretical calculations with no fitting parameters, including the dynamics' dependence on molecule number and on the dipolar interaction strength. This agreement verifies the microscopic model expected to govern the dynamics of dipolar molecules, even in this strongly correlated beyond-mean-field regime, and represents the first step towards using this system to explore many-body dynamics in regimes that are inaccessible to current theoretical techniques.
Understanding many-body physics in one dimension from the Liebâ€“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 Liebâ€“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 Betheâ€™s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Liebâ€“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 Yangâ€“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 Liebâ€“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 Î³ , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient DR â€”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 Î³ , 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 DRËœÎ³-2 , 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
NASA Astrophysics Data System (ADS)
Medders, Gregory R.; Götz, Andreas W.; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-01
Recent work has shown that the many-body expansion of the interaction energy 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. 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 water interactions from the gas to the condensed phase. Similarly, 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.
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.
On the representation of many-body interactions in water.
Medders, Gregory R; Götz, Andreas W; Morales, Miguel A; Bajaj, Pushp; Paesani, Francesco
2015-09-14
Recent work has shown that the many-body expansion of the interaction energy 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. 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 water interactions from the gas to the condensed phase. Similarly, 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. PMID:26374013
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.
Identifying the local conserved quantities in Many-Body-Localized matter
NASA Astrophysics Data System (ADS)
Pekker, David; Tian, Binbin; Yu, Xiongji; Clark, Bryan; Oganesyan, Vadim
2015-05-01
Typically, many-body systems with interactions tend to thermalize. However, adding sufficient disorder (or possibly via other mechanisms) one can induce many-body localization. The localization occurs by the spontaneous appearance of local conserved quantities. We describe how to identify these conserved quantities and explore their localization properties. We also comment on how these conserved quantities are reflected in cold atom experiments on localized matter.
Particle diagrams and statistics of many-body random potentials
NASA Astrophysics Data System (ADS)
Small, Rupert A.; MÃ¼ller, 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 â‰¤ 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 â‰ª m â‰ª 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 , â€¦ , nk for the 2 nth moment.
Total correlations of the diagonal ensemble herald the many-body localization transition
NASA Astrophysics Data System (ADS)
Goold, J.; Gogolin, C.; Clark, S. R.; Eisert, J.; Scardicchio, A.; Silva, A.
2015-11-01
The intriguing phenomenon of many-body localization (MBL) has attracted significant interest recently, but a complete characterization is still lacking. In this work we introduce the total correlations, a concept from quantum information theory capturing multipartite correlations, to the study of this phenomenon. We demonstrate that the total correlations of the diagonal ensemble provides a meaningful diagnostic tool to pin-down, probe, and better understand the MBL transition and ergodicity breaking in quantum systems. In particular, we show that the total correlations has sublinear dependence on the system size in delocalized, ergodic phases, whereas we find that it scales extensively in the localized phase developing a pronounced peak at the transition. We exemplify the power of our approach by means of an exact diagonalization study of a Heisenberg spin chain in a disordered field. By a finite size scaling analysis of the peak position and crossover point from log to linear scaling we collect evidence that ergodicity is broken before the MBL transition in this model.
Energy benchmarks for water clusters and ice structures from an embedded many-body expansion
NASA Astrophysics Data System (ADS)
Gillan, M. J.; Alfè, D.; Bygrave, P. J.; Taylor, C. R.; Manby, F. R.
2013-09-01
We show how an embedded many-body expansion (EMBE) can be used to calculate accurate ab initio energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave et al. [J. Chem. Phys. 137, 164102 (2012)], in which the terms in the expansion are obtained from calculations on monomers, dimers, etc., acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order Møller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 mEh/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II, and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested.
Energy benchmarks for water clusters and ice structures from an embedded many-body expansion.
Gillan, M J; Alfè, D; Bygrave, P J; Taylor, C R; Manby, F R
2013-09-21
We show how an embedded many-body expansion (EMBE) can be used to calculate accurate ab initio energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave et al. [J. Chem. Phys. 137, 164102 (2012)], in which the terms in the expansion are obtained from calculations on monomers, dimers, etc., acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order Møller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 mE(h)/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II, and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested. PMID:24070273
NASA Astrophysics Data System (ADS)
Makkonen, Ilja; Ervasti, Mikko M.; Siro, Topi; Harju, Ari
2014-01-01
The correlated motion of a positron surrounded by electrons is a fundamental many-body problem. We approach this by modeling the momentum density of annihilating electron-positron pairs using the framework of reduced density matrices, natural orbitals, and natural geminals (electron-positron pair wave functions) of the quantum theory of many-particle systems. We find that an expression based on the natural geminals provides an exact, unique, and compact expression for the momentum density. The natural geminals can be used to define and to determine enhancement factors for enhancement models going beyond the independent-particle model for a better understanding of the results of positron annihilation experiments.
Hamiltonian tomography: the quantum (system) measurement problem
NASA Astrophysics Data System (ADS)
Cole, Jared H.
2015-10-01
To harness the power of controllable quantum systems for information processing or quantum simulation, it is essential to be able to accurately characterise the system's Hamiltonian. Although in principle this requires determining less parameters than full quantum process tomography, a general and extendable method for reconstructing a general Hamiltonian has been elusive. In their recent paper, Wang et al (2015 New J. Phys. 17 093017) apply dynamical decoupling to the problem of Hamiltonian tomography and show how to reconstruct a general many-body Hamiltonian comprised of arbitrary interactions between qubits.
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 effects in silicene, silicane, germanene and germanane.
Wei, Wei; Dai, Ying; Huang, Baibiao; Jacob, Timo
2013-06-14
Silicene, which is the silicon equivalent of carbon-based graphene and shares some of the unique properties with graphene, has been attracting more and more attention since its synthesis and represents a breakthrough in current silicon-based technology. In this work, many-body effects in silicene, silicane, germanene and germanane have been demonstrated based on the Green's function perturbation theory, i.e., GW + Bethe-Salpeter equation. Due to confinement, many-body effects play a pivotal role in quasi-particle excitations and optical absorption spectra, which leads to excitonic resonance (???* excitation) in silicene and germanene, and strongly bound excitons in silicane and germanane with considerable binding energies. PMID:23640017
Competing many-body instabilities and unconventional superconductivity in graphene
NASA Astrophysics Data System (ADS)
Kiesel, Maximilian L.; Platt, Christian; Hanke, Werner; Abanin, Dmitry A.; Thomale, Ronny
2012-07-01
The band structure of graphene exhibits van Hove singularities (VHSs) at dopings x=±1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases. We study the competition between many-body instabilities in graphene using the functional renormalization group. We predict a rich phase diagram, which, depending on band structure as well as the range and scale of Coulomb interactions, contains a d+id-wave superconducting (SC) phase, or a spin-density-wave phase at the VHS. The d+id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. Nearby the VHS, we find singlet d+id-wave and triplet f-wave SC phases.
Competing many-body instabilities and unconventional superconductivity in graphene
NASA Astrophysics Data System (ADS)
Platt, Christian; Kiesel, Maximilian; Hanke, Werner; Abanin, Dmitry A.; Thomale, Ronny
2012-02-01
The band structure of graphene exhibits van Hove singularities (VHS) at doping x = ±1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d + id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d + id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d + id-wave as well as triplet f -wave SC phases. [4pt] [1] arXiv:1109.2953v1
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.
Automatic Generation of Vacuum Amplitude Many-Body Perturbation Series
NASA Astrophysics Data System (ADS)
Stevenson, P. D.
An algorithm and a computer program in Fortran 95 are presented which enumerate the Hugenholtz diagram representation of the many-body perturbation series for the ground state energy with a two-body interaction. The output is in a form suitable for post-processing such as automatic code generation. The result of a particular application, generation of LATEX code to draw the diagrams, is shown.
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 representationmoreÂ Â» 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.Â«Â less
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 Grünberg, 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.
Three-body decay of many-body resonances
Jensen, A.S.; Fedorov, D.V.; Fynbo, H.O.U.; Garrido, E.
2005-10-14
We use the hyperspherical coordinates to describe decay of many-body resonances. Direct and sequential decay are described by different paths in the distances between the particles. We generalize the WKB expression for the {alpha}-decay width to decay of three charged particles. Decay mechanisms and resonance structures are computed in coordinate space. The energy distributions of the particles after decay are discussed. Moderate s-wave scattering lengths prefer decay via corresponding virtual state possibly leaving unique fingerprints of this reminiscence of the Efimov effect in the decay of excited states. Numerical illustrations are resonances in 6He, 12C, 17Ne.
NASA Astrophysics Data System (ADS)
Beinke, Raphael; Klaiman, Shachar; Cederbaum, Lorenz S.; Streltsov, Alexej I.; Alon, Ofir E.
2015-10-01
In this work, we study the out-of-equilibrium many-body tunneling dynamics of a Bose-Einstein condensate in a two-dimensional radial double well. We investigate the impact of interparticle repulsion and compare the influence of angular momentum on the many-body tunneling dynamics. Accurate many-body dynamics are obtained by solving the full many-body Schrödinger equation. We demonstrate that macroscopic vortex states of definite total angular momentum indeed tunnel and that, even in the regime of weak repulsions, a many-body treatment is necessary to capture the correct tunneling dynamics. As a general rule, many-body effects set in at weaker interactions when the tunneling system carries angular momentum.
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-? always leads to the localization breakdown in a thermodynamic limit of an infinite system at ? <3 d /2 where d is a system dimension. The delocalization takes place due to the induced Ising interactions U (R ) ?R-2 ? 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 ? ?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 mobility edge due to symmetry-constrained dynamics and strong interactions
NASA Astrophysics Data System (ADS)
Mondragon-Shem, Ian; Pal, Arijeet; Hughes, Taylor L.; Laumann, Chris R.
2015-08-01
We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1 /2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and antiferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.
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.
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
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.
TOPICAL REVIEW: Intense-field many-body S-matrix theory
NASA Astrophysics Data System (ADS)
Becker, A.; Faisal, F. H. M.
2005-02-01
Intense-field many-body S-matrix theory (IMST) provides a systematic ab initio approach to investigate the dynamics of atoms and molecules interacting with intense laser radiation. We review the derivation of IMST as well as its diagrammatic representation and point out its advantage over the conventional 'prior' and 'post' expansions which are shown to be special cases of IMST. The practicality and usefulness of the theory is illustrated by its application to a number of current problems of atomic and molecular ionization in intense fields. We also present a consistent S-matrix formulation of the quantum amplitude for high harmonic generation (HHG) and point out some of the most general properties of HHG radiation emitted by a single atom as well as its relation to coherent emission from many atoms. Experimental results for single and double (multiple) ionization of atoms and the observed distributions of coincidence measurements are analysed and the dominant mechanisms behind them are discussed. Ionization of more complex systems such as diatomic and polyatomic molecules in intense laser fields is analysed as well using IMST and the results are discussed with special attention to the role of molecular orbital symmetry and molecular orientation in space. The review ends with a summary and a brief outlook.
Benchmark Many-Body GW and Bethe-Salpeter Calculations for Small Transition Metal Molecules.
Körbel, Sabine; Boulanger, Paul; Duchemin, Ivan; Blase, Xavier; Marques, Miguel A L; Botti, Silvana
2014-09-01
We study the electronic and optical properties of 39 small molecules containing transition metal atoms and 7 others related to quantum-dots for photovoltaics. We explore in particular the merits of the many-body GW formalism, as compared to the ?SCF approach within density functional theory, in the description of the ionization energy and electronic affinity. Mean average errors of 0.2-0.3 eV with respect to experiment are found when using the PBE0 functional for ?SCF and as a starting point for GW. The effect of partial self-consistency at the GW level is explored. Further, for optical excitations, the Bethe-Salpeter formalism is found to offer similar accuracy as time-dependent DFT-based methods with the hybrid PBE0 functional, with mean average discrepancies of about 0.3 and 0.2 eV, respectively, as compared to available experimental data. Our calculations validate the accuracy of the parameter-free GW and Bethe-Salpeter formalisms for this class of systems, opening the way to the study of large clusters containing transition metal atoms of interest for photovoltaic applications. PMID:26588537
First-principles energetics of water clusters and ice: A many-body analysis
Gillan, M. J.; AlfÃ¨, 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 ; BartÃ³k, A. P.; CsÃ¡nyi, 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.
Many-body effects in topological Kondo insulators
NASA Astrophysics Data System (ADS)
Iaconis, Jason; Balents, Leon
2015-06-01
We study the effect of interactions on the properties of a model 2D topological Kondo insulator phase. Loosely motivated by recent proposals where graphene is hybridized with impurity bands from heavy adatoms with partially filled d shells, we introduce a model Hamiltonian which we believe captures the essential physics of the different competing phases. We show that there are generically three possible phases with different combinations of Kondo screening and magnetic order. Perhaps the most dramatic example of many-body physics in symmetry-protected topological phases is the existence of the exotic edge states. We demonstrate that our mean-field model contains a region with a time-reversal-invariant bulk phase but where time-reversal symmetry is spontaneously broken at the edge. Such a phase would not be possible in a noninteracting model. We also comment on the stability of this phase beyond mean-field theory.
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.
The electron many-body problem in graphene
NASA Astrophysics Data System (ADS)
Uchoa, Bruno; Reed, James P.; Gan, Yu; Joe, Young, II; Fradkin, Eduardo; Abbamonte, Peter; Casa, Diego
2012-01-01
We give a brief summary of the current status of the electron many-body problem in graphene. We claim that graphene has intrinsic dielectric properties which should dress the interactions among the quasiparticles, and may explain why the observation of electron-electron renormalization effects has been so elusive in the recent experiments. We argue that the strength of Coulomb interactions in graphene may be characterized by an effective fine structure constant given by ?star(k, ?)?2.2/epsilon(k, ?), where epsilon(k, ?) is the dynamical dielectric function. At long wavelengths, ?star(k, ?) appears to have its smallest value in the static regime, where ?star(k?0, 0)?1/7 according to recent inelastic x-ray measurements, and the largest value in the optical limit, where ?star(0, ?)?2.6. We conclude that the strength of Coulomb interactions in graphene is not universal, but is highly dependent on the scale of the phenomenon of interest. We propose a prescription in order to reconcile different experiments.
Many-body central force potentials for tungsten
NASA Astrophysics Data System (ADS)
Bonny, G.; Terentyev, D.; Bakaev, A.; Grigorev, P.; Van Neck, D.
2014-07-01
Tungsten and tungsten-based alloys are the primary candidate materials for plasma facing components in fusion reactors. The exposure to high-energy radiation, however, severely degrades the performance and lifetime limits of the in-vessel components. In an effort to better understand the mechanisms driving the materials' degradation at the atomic level, large-scale atomistic simulations are performed to complement experimental investigations. At the core of such simulations lies the interatomic potential, on which all subsequent results hinge. In this work we review 19 central force many-body potentials and benchmark their performance against experiments and density functional theory (DFT) calculations. As basic features we consider the relative lattice stability, elastic constants and point-defect properties. In addition, we also investigate extended lattice defects, namely: free surfaces, symmetric tilt grain boundaries, the 1/2<1?1?1>{1?1?0} and 1/2<1?1?1> {1?1?2} stacking fault energy profiles and the 1/2<1?1?1> screw dislocation core. We also provide the Peierls stress for the 1/2<1?1?1> edge and screw dislocations as well as the glide path of the latter at zero Kelvin. The presented results serve as an initial guide and reference list for both the modelling of atomically-driven phenomena in bcc tungsten, and the further development of its potentials.
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-? 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.
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.
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
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 ??n=2a?\\dot n?n+2?m =1,m?nN(?\\dot n-a?n2)(?\\dot m-a?m2)/(?n-?m), 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 ??n-3i?\\zdot n-2?2zn=2a(\\zdot n-i?zn)zn+2?m =1,m?nN(\\zdot n-i?zn-azn2)(\\zdot m-i?zm-azm2)/(zn-zm), n =1,…,N, where ? 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 =2?/? 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.
Krishtal, Alisa; Sinha, Debalina; Genova, Alessandro; Pavanello, Michele
2015-05-13
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. PMID:25880118
Many-body renormalization of the minimal conductivity in graphene.
Guinea, F; Katsnelson, M I
2014-03-21
The conductance of ballistic graphene at the neutrality point is due to coherent electron tunneling between the leads, the so called pseudodiffusive regime. The conductance scales as a function of the sample dimensions in the same way as in a diffusive metal, despite the difference in the physical mechanisms involved. The electron-electron interaction modifies this regime, and plays a role similar to that of the environment in macroscopic quantum phenomena. We show that interactions can change substantially the transport properties. In the presence of nearby metallic layers, the conductance near the neutrality point can decrease with decreasing temperature, and reach values well below the quantum unit of conductance, as in an insulator. PMID:24702399
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.
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
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 Î± â‰ƒ2 /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.
Many-body localization and mobility edge in a disordered spin-1/2 Heisenberg ladder
NASA Astrophysics Data System (ADS)
Baygan, Elliott; Lim, S. P.; Sheng, D. N.
2015-11-01
We examine the interplay of interaction and disorder for a Heisenberg spin-1/2 ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the dynamic phase transition at a critical random field strength hc˜8.5 ±0.5 , where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuations of the bipartite magnetization show distinct probability distributions which characterize different phases. Furthermore, we show that for weaker h , energy eigenstates with higher-energy density are delocalized while states at lower-energy density are localized, which defines a mobility edge separating these two phases. With increasing disorder strength, the mobility edge moves towards higher-energy density, which drives the system to the phase of the full many-body localization.
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.
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.
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/ .
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.
NASA Astrophysics Data System (ADS)
Monthus, CÃ©cile
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 â‰¤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.
Equation of state for expanded fluid mercury: variational theory with many-body interaction.
Kitamura, Hikaru
2007-04-01
A variational associating fluid theory is proposed to describe equations of state for expanded fluid mercury. The theory is based on the soft-sphere variational theory, incorporating an ab initio diatomic potential and an attractive many-body potential; the latter is evaluated with quantum chemical methods and expressed as a function of the local atomic coordination number and the nearest-neighbor distance. The resultant equation of state can reproduce the observed gas-liquid coexistence curve with good accuracy, without introducing phenomenological effective pair potentials. Various thermodynamic quantities such as pressure, isocloric thermal pressure coefficient, adiabatic sound velocity, and specific heat are calculated over a wide density-temperature range and compared with available experimental data. PMID:17430049
The role of attractive many-body interaction in the gas-liquid transition of mercury.
Kitamura, Hikaru
2007-02-21
The equation of state for expanded fluid mercury based on the variational associating fluid theory is developed to elucidate the mechanisms of the gas-liquid transition in terms of microscopic interatomic interaction. The theory describes the interaction of an atom with its neighbouring atoms through an effective many-body potential, which is constructed through quantum-chemical calculations of cohesive energies for selected geometries of clusters and bulk crystals. The overall feature of the observed gas-liquid coexistence curve is reproduced accurately without introducing phenomenological adjustable parameters. It is shown that the local aggregation of atoms produces a strong cohesive force due to a change in the local electronic states, which plays a crucial role in the gas-liquid transition. The predicted phase behaviour is consistent with the picture of inhomogeneous expansion, in which the average coordination number is nearly proportional to the average density along the coexistence curve. PMID:22251578
Anomalous diffusion and griffiths effects near the many-body localization transition.
Agarwal, Kartiek; Gopalakrishnan, Sarang; Knap, Michael; Müller, Markus; Demler, Eugene
2015-04-24
We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features. PMID:25955037
Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition
NASA Astrophysics Data System (ADS)
Agarwal, Kartiek; Gopalakrishnan, Sarang; Knap, Michael; Müller, Markus; Demler, Eugene
2015-04-01
We explore the high-temperature dynamics of the disordered, one-dimensional X X Z model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.
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 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
Periodic thermodynamics of isolated quantum systems.
Lazarides, Achilleas; Das, Arnab; Moessner, Roderich
2014-04-18
The nature of the behavior of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient period, such a system is known to synchronize with the driving; in contrast to the nondriven case, no fundamental principle has been proposed for constructing the resulting nonequilibrium state. Here, we analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which we explicitly identify. This result constitutes a generalization of the concepts of equilibrium statistical mechanics to a class of far-from-equilibrium systems, up to now mainly accessible using ad hoc methods. PMID:24785013
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.
Itinerant type many-body theories for photo-induced structural phase transitions
NASA Astrophysics Data System (ADS)
Nasu, Keiichiro
2004-09-01
Itinerant type quantum many-body theories for photo-induced structural phase transitions (PSPTs) are reviewed in close connection with various recent experimental results related to this new optical phenomenon. There are two key concepts: the hidden multi-stability of the ground state, and the proliferations of optically excited states. Taking the ionic (I) rarr neutral (N) phase transition in the organic charge transfer (CT) crystal, TTF-CA, as a typical example for this type of transition, we, at first, theoretically show an adiabatic path which starts from CT excitons in the I-phase, but finally reaches an N-domain with a macroscopic size. In connection with this I-N transition, the concept of the initial condition sensitivity is also developed so as to clarify experimentally observed nonlinear characteristics of this material. In the next, using a more simplified model for the many-exciton system, we theoretically study the early time quantum dynamics of the exciton proliferation, which finally results in the formation of a domain with a large number of excitons. For this purpose, we derive a stepwise iterative equation to describe the exciton proliferation, and clarify the origin of the initial condition sensitivity. Possible differences between a photo-induced nonequilibrium phase and an equilibrium phase at high temperatures are also clarified from general and conceptional points of view, in connection with recent experiments on the photo-induced phase transition in an organo-metallic complex crystal. It will be shown that the photo-induced phase can make a new interaction appear as a broken symmetry only in this phase, even when this interaction is almost completely hidden in all the equilibrium phases, such as the ground state and other high-temperature phases. The relation between the photo-induced nonequilibrium phase and the hysteresis induced nonequilibrium one is also qualitatively discussed. We will be concerned with a macroscopic parity violation and a ferro- (or super-para-) electricity, induced by a photogenerated electron in the perovskite type quantum dielectric SrTiO3. The photogenerated electron in the 3d band of Ti is assumed to couple weakly, but quadratically, with soft-anharmonic T1u phonons, and strongly but linearly to the breathing (A1g) type high energy phonons. These two types of electron-phonon coupling result in two types of polarons, a super-para-electric (SPE) large polaron with a quasi-global parity violation, and an off-centre type self-trapped polaron with only a local parity violation. This SPE large polaron, being equal to a charged and conductive ferroelectric domain, greatly enhances both the quasi-static electric susceptibility and the electronic conductivity. We also briefly review recent successes to observe the PSPTs more directly by using x-ray measurements.
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.
Exact scattering eigenstates in double quantum-dot systems with an interdot Coulomb interaction
NASA Astrophysics Data System (ADS)
Nishino, Akinori; Hatano, Naomichi; Ordonez, Gonzalo
2016-01-01
We study a double quantum-dot system which consists of two leads of noninteracting electrons and two quantum dots with an interdot Coulomb interaction. We assume spinless electrons and consider arbitrary complex values of all lead-dot couplings and an interdot coupling. We construct exact many-electron scattering eigenstates whose incident states are free-electronic plane waves in the leads. Due to the interaction, some of the incident plane waves are scattered to two-body and three-body bound states. The binding strength of the many-body bound states is affected by the arrangement of the two quantum dots, by which we observe an interplay of the Coulomb interaction and quantum interference. We can understand the many-body bound states in terms of many-body resonances.
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.
Relativistic many-body calculation of low-energy dielectronic resonances in Be-like carbon
Derevianko, A.; Dzuba, V. A.; Kozlov, M. G.
2010-08-15
We apply the relativistic configuration-interaction method coupled with the many-body perturbation theory (CI+MBPT) to describe low-energy dielectronic recombination. We combine the CI+MBPT approach with the complex rotation method (CRM) and compute the dielectronic recombination spectrum for Li-like carbon, which recombines into Be-like carbon. We demonstrate the utility and evaluate the accuracy of this newly developed CI+MBPT+CRM approach by comparing our results with the results of the previous high-precision study of the Ciii system [Mannervik et al., Phys. Rev. Lett. 81, 313 (1998)].
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.
NASA Astrophysics Data System (ADS)
Cahill, Reginald T.
2002-10-01
So far proposed quantum computers use fragile and environmentally sensitive natural quantum systems. Here we explore the new notion that synthetic quantum systems suitable for quantum computation may be fabricated from smart nanostructures using topological excitations of a stochastic neural-type network that can mimic natural quantum systems. These developments are a technological application of process physics which is an information theory of reality in which space and quantum phenomena are emergent, and so indicates the deep origins of quantum phenomena. Analogous complex stochastic dynamical systems have recently been proposed within neurobiology to deal with the emergent complexity of biosystems, particularly the biodynamics of higher brain function. The reasons for analogous discoveries in fundamental physics and neurobiology are discussed.
How does an isolated quantum system relax?
NASA Astrophysics Data System (ADS)
Schmiedmayer, Joerg
2014-03-01
One of the biggest challenges in probing non-equilibrium dynamics of many-body quantum systems is that there is no general approach to characterize the resulting quantum states. Interference experiments give access to the phase of the order parameter. The full distribution functions of the interference amplitude, and the full phase correlation functions allow us to study the relaxation dynamics in one-dimensional quantum systems. Starting form a coherently split 1d quantum gas, the initial coherence slowly decays. Due to the approximate conserved quantities in our nearly integrable system, this relaxation leads to a pre-thermalized state, which is characterized by thermal like distribution functions but exhibits an effective temperature much lower than the kinetic temperature of the initial system. A detailed study of the correlation functions reveals that these thermal-like properties emerge locally in their final form and propagate through the system in a light-cone-like evolution. Furthermore we demonstrate that the pre- thermalized state is connected to a Generalized Gibbs Ensemble and show the pathways for further relaxation towards thermal equilibrium. Supported by the Austrian Science Foundation and the European Research Council ERC AdG: Quantum Relax
Electro-optic and Many-body Effects on Optical Absorption of Twisted Bilayer Graphene
NASA Astrophysics Data System (ADS)
Lee, Kan-Heng; Huang, Lujie; Kim, Cheol-Joo; Park, Jiwoong
2015-03-01
In twisted bilayer graphene (tBLG), the interlayer rotation angle between the two graphene layers induces additional angle-dependent van Hove singularities (vHSs) in its band structure where the two Dirac cones from each layer intersect. These vHSs introduce extra angle-dependent absorption peaks in the optical absorption spectra of tBLG. Here, we experimentally investigate the effects of the overall doping and the interlayer potential on these interlayer absorption features at various angles. We independently tune the doping concentration of each layer with a newly-developed, optically transparent, dual-gate transistor geometry to perform simultaneous optical and electrical measurements. Our data show strong electro-optic phenomena in the optical absorption of tBLG: the peak energy and width of the interlayer resonance feature sensitively depends on the overall doping and interlayer potential. We explain our observation using a simple band picture as well as many-body effects. Our study provides a powerful experimental platform for studying more complicated structures such as rotated tri- and multi-layer graphene systems in the future. Moreover, the understanding of electro-optic and many-body effects in these materials opens up a way for novel electrochromic devices.
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 Ã…. The results of this study hold the promise for potential applications of the GeC hybrid in optoelectronics.
Many-Body Localization in One Dimension as a Dynamical Renormalization Group Fixed Point
NASA Astrophysics Data System (ADS)
Vosk, Ronen; Altman, Ehud
2013-02-01
We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as log?log?t found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.
Accurate and Efficient Method for Many-Body van der Waals Interactions
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre; DiStasio, Robert A., Jr.; Car, Roberto; Scheffler, Matthias
2012-06-01
An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap molecules and solids. This is achieved by combining the Tkatchenko-Scheffler van der Waals (vdW) method [Phys. Rev. Lett. 102, 073005 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.073005] with the self-consistent screening equation of classical electrodynamics. This leads to a seamless description of polarization and depolarization for the polarizability tensor of molecules and solids. The screened long-range many-body vdW energy is obtained from the solution of the Schrödinger equation for a system of coupled oscillators. We show that the screening and the many-body vdW energy play a significant role even for rather small molecules, becoming crucial for an accurate treatment of conformational energies for biomolecules and binding of molecular crystals. The computational cost of the developed theory is negligible compared to the underlying electronic structure calculation.
Many-Body Effects on the Thermodynamics of Fluids, Mixtures, and Nanoconfined Fluids.
Desgranges, Caroline; Delhommelle, Jerome
2015-11-10
Using expanded Wang-Landau simulations, we show that taking into account the many-body interactions results in sharp changes in the grand-canonical partition functions of single-component systems, binary mixtures, and nanoconfined fluids. The many-body contribution, modeled with a 3-body Axilrod-Teller-Muto term, results in shifts toward higher chemical potentials of the phase transitions from low-density phases to high-density phases and accounts for deviations of more than, e.g., 20% of the value of the partition function for a single-component liquid. Using the statistical mechanics formalism, we analyze how this contribution has a strong impact on some properties (e.g., pressure, coexisting densities, and enthalpy) and a moderate impact on others (e.g., Gibbs or Helmholtz free energies). We also characterize the effect of the 3-body terms on adsorption isotherms and adsorption thermodynamic properties, thereby providing a full picture of the effect of the 3-body contribution on the thermodynamics of nanoconfined fluids. PMID:26574329
Chmela, JiÅ™Ã; 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
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
Controlling many-body states by the electric-field effect in a two-dimensional material
NASA Astrophysics Data System (ADS)
Li, L. J.; Oâ€™Farrell, E. C. T.; Loh, K. P.; Eda, G.; Ã–zyilmaz, B.; Castro Neto, A. H.
2016-01-01
To understand the complex physics of a system with strong electronâ€“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 170â€‰kelvin to 40â€‰kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0â€‰kelvin up to 3â€‰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 Littleâ€“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; Ã–zyilmaz, 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 170â€‰kelvin to 40â€‰kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0â€‰kelvin up to 3â€‰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)
Bäppler, Stefanie A.; Plasser, Felix; Wormit, Michael; Dreuw, Andreas
2014-11-01
Exciton sizes and electron-hole binding energies, which are central properties of excited states in extended systems and crucial to the design of modern electronic devices, are readily defined within a quasiparticle framework but are quite challenging to understand in the molecular-orbital picture. The intent of this work is to bridge this gap by providing a general way of extracting the exciton wave function out of a many-body wave function obtained by a quantum chemical excited-state computation. This methodology, which is based on the one-particle transition density matrix, is implemented within the ab initio algebraic diagrammatic construction scheme for the polarization propagator and specifically the evaluation of exciton sizes, i.e., dynamic charge separation distances, is considered. A number of examples are presented. For stacked dimers it is shown that the exciton size for charge separated states corresponds to the intermolecular separation, while it only depends on the monomer size for locally excited states or Frenkel excitons. In the case of conjugated organic polymers, the tool is applied to analyze exciton structure and dynamic charge separation. Furthermore, it is discussed how the methodology may be used for the construction of a charge-transfer diagnostic for time-dependent density-functional theory.
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 Localization in the Presence of a Single-Particle Mobility Edge.
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. PMID:26684100
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.
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 processes in black and gray matter-wave solitons
NASA Astrophysics Data System (ADS)
KrÃ¶nke, 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.
Half-metallic ferromagnets: From band structure to many-body effects
NASA Astrophysics Data System (ADS)
Katsnelson, M. I.; Irkhin, V. Yu.; Chioncel, L.; Lichtenstein, A. I.; de Groot, R. A.
2008-04-01
A review of new developments in theoretical and experimental electronic-structure investigations of half-metallic ferromagnets (HMFs) is presented. Being semiconductors for one spin projection and metals for another, these substances are promising magnetic materials for applications in spintronics (i.e., spin-dependent electronics). Classification of HMFs by the peculiarities of their electronic structure and chemical bonding is discussed. The effects of electron-magnon interaction in HMFs and their manifestations in magnetic, spectral, thermodynamic, and transport properties are considered. Special attention is paid to the appearance of nonquasiparticle states in the energy gap, which provide an instructive example of essentially many-body features in the electronic structure. State-of-the-art electronic calculations for correlated d -systems are discussed, and results for specific HMFs (Heusler alloys, zinc-blende structure compounds, CrO2 , and Fe3O4 ) are reviewed.
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.
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 Ã…. The results of this work make silicene-graphene hybrid a promising candidate for optoelectronic applications.
Optical spectra from molecules to crystals: Insight from many-body perturbation theory
NASA Astrophysics Data System (ADS)
Cocchi, Caterina; Draxl, Claudia
2015-11-01
Time-dependent density-functional theory (TDDFT) often successfully reproduces excitation energies of finite systems, already in the adiabatic local-density approximation (ALDA). Here we show for prototypical molecular materials, i.e., oligothiophenes, that ALDA largely fails, and we explain why this is so. By comparing TDDFT with an in-depth analysis based on many-body perturbation theory, we demonstrate that correlation effects have a crucial impact on the energies and character of the optical excitations, not only for molecules of increasing length and in a crystalline environment but even for isolated small molecules. We argue that only high-level methodologies, which explicitly include correlation effects, can reproduce optical spectra of molecular materials with equal accuracy from gas phase to crystal structures.
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 layersâ€”regions surrounding the particles where non-equilibrium processes produce large velocity gradientsâ€”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 â€˜self-assembled pumpâ€™, are (a) one-body self-propulsion and (b) two-body rotation from the vorticity of the Stokeslet induced in the trap.
Can high magnetic fields enhance many-body effects in organic conductors?
NASA Astrophysics Data System (ADS)
McKenzie, Ross H.
1997-03-01
Conducting organic molecular crystals based on the BEDT-TTF and TMTSF molecules are novel low-dimensional electronic systems. They exhibit a subtle competition between metallic, superconducting, and density-wave phases. This competition is sensitive to anion type, temperature, pressure, uniaxial stress, and magnetic field. A general introduction will be given to these exciting materials with an emphasis on the different energy scales that play a role in magnetotransport in the metallic phases. It will be discussed how in quasi-one-dimensional systems high fields can reduce the dimensionality and enhance fluctuations and many-body effects.(Y.M. Yakovenko, Sov. Phys. JETP 66), 355 (1987); R.H. McKenzie, Phys. Rev. Lett. 74, 5140 (1995). Examples of experimental data which has a relatively simple explanation in terms of an anisotropic Fermi liquid will be contrasted to data which does not appear to have a straight-forward explanation in terms of a single-particle picture. Specific examples to be considered include (i) longitudinal magnetoresistance in the TMTSF salts(J.S. Brooks et al., Phys. Rev. B 53), 14406 (1996); G.M. Danner and P.M. Chaikin, Phys. Rev. Lett., to appear. (ii) the effect of magnetic breakdown on magnetoresistance in the quasi-two-dimensional salts (BEDT-TTF)_2MHg(SCN)_4[M=K,Rb,Tl](R.H. McKenzie et al., Phys. Rev. B 54), R8289 (1996). and (iii) the deviation of magneto-oscillations in (BEDT-TTF)_2NH_4Hg(SCN)4 from the predictions of Lifshitz-Kosevich theory.(N. Harrison et al., Phys. Rev. B 54), 9977 (1996); R.H. McKenzie et al., Surf. Sci. 362, 901 (1996). A major point of this pedagogical talk is that although these fascinating materials exhibit some puzzling behavior one should be cautious before invoking explanations in terms of many-body effects.
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 dimensionalityâ€”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, SÃ¸ren Ulstrup, Marco Bianchi, Richard Hatch, Dandan Guan, Federico Mazzola, Liv HornekÃ¦r, 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 CortÃ©s, 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 FÃ¨vre, F Bertran and A Taleb-Ibrahimi What about U on surfaces? Extended Hubbard models for adatom systems from first principlesPhilipp Hansmann, LoÃ¯g Vaugier, Hong Jiang and Silke Biermann Influence of on-site Coulomb interaction U on properties of MnO(001)2 Ã— 1 and NiO(001)2 Ã— 1 surfacesA SchrÃ¶n, M Granovskij and F Bechstedt On the organic energy gap problemF Flores, E Abad, J I MartÃnez, 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.
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 Greenâ€™s function, demonstrating the â€˜failureâ€™ 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.
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
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.
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.
Numerical analysis of coherent many-body currents in a single atom transistor
Daley, A.J.; Zoller, P.; Clark, S.R.; Jaksch, D.
2005-10-15
We study the dynamics of many atoms in the recently proposed single-atom-transistor setup [A. Micheli, A. J. Daley, D. Jaksch, and P. Zoller, Phys. Rev. Lett. 93, 140408 (2004)] using recently developed numerical methods. In this setup, a localized spin-1/2 impurity is used to switch the transport of atoms in a one-dimensional optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a single-atom mirror. We calculate time-dependent currents for bosons passing the impurity atom, and find interesting many-body effects. These include substantially different transport properties for bosons in the strongly interacting (Tonks) regime when compared with fermions, and an unexpected decrease in the current when weakly interacting probe atoms are initially accelerated to a nonzero mean momentum. We also provide more insight into the application of our numerical methods to this system, and discuss open questions about the currents approached by the system on long time scales.
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.
Unphysical and physical solutions in many-body theories: from weak to strong correlation
NASA Astrophysics Data System (ADS)
Stan, Adrian; Romaniello, Pina; Rigamonti, Santiago; Reining, Lucia; Berger, J. A.
2015-09-01
Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of nonlinear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Green’s function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Green’s function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.
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.
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.
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.
Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems
NASA Astrophysics Data System (ADS)
Cohen, Guy; Gull, Emanuel; Reichman, David R.; Millis, Andrew J.
2015-12-01
Current nonequilibrium Monte Carlo methods suffer from a dynamical sign problem that makes simulating real-time dynamics for long times exponentially hard. We propose a new "inchworm algorithm," based on iteratively reusing information obtained in previous steps to extend the propagation to longer times. The algorithm largely overcomes the dynamical sign problem, changing the scaling from exponential to quadratic. We use the method to solve the Anderson impurity model in the Kondo and mixed valence regimes, obtaining results both for quenches and for spin dynamics in the presence of an oscillatory magnetic field.
Anisotropic magnetic interactions in 5d iridium oxides by many-body quantum chemistry calculations
NASA Astrophysics Data System (ADS)
Katukuri, Vamshi M.; Nishimoto, Satoshi; Yushankhai, Viktor; Rousochatzakis, Ioannis; Hozoi, Liviu; van den Brink, Jeroen
2014-03-01
Ir 5d5 oxides are being actively studied due to the realization of novel spin-orbit coupled jeff ~ 1/2 ground states. One remarkable feature in these compounds is the highly anisotropic magnetic interactions, orders of magnitude stronger than in 3d oxides. We address the nature of the anisotropic exchange in the 2D honeycomb (Na/Li)2IrO3 ((Na/Li)213) and square-lattice (Sr/Ba)2IrO4 ((Sr/Ba)213) iridates, by ab initio multireference configuration-interaction calculations on large embedded clusters. For Na213 we find that the Kitaev term is ferromagnetic and defines the dominant energy scale while the nearest-neighbor Heisenberg contribution is antiferromagnetic. Although Li213 is structurally similar, we predict quite different set of interaction parameters in Li213. We further analyze the magnetic order and the essential differences between these two materials by exact diagonalization and density-matrix renormalization-group calculations that additionally include 2nd and 3rd neighbor couplings. Sizable symmetric anisotropic interactions are also computed for Ba214. From the ab initio data, the relevant in-plane spin model for Ba214 turns out to be a Heisenberg-compass effective model. We finally discuss the Dzyaloshinskii-Moriya exchange in Sr214.
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.
NASA Astrophysics Data System (ADS)
SchrÃ¶der, 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.
Theoretical Studies of Surfaces, Clusters, and the Many-Body Problem Using Semiempirical Models
NASA Astrophysics Data System (ADS)
Streszewski, Marcin
Hydrogen chemisorption, the magnetism of small metal clusters, and the many-body problem were studied with the use of the Hubbard Hamiltonian. The chemisorption of hydrogen on transition metals was studied within the unrestricted Hartree-Fock approximation. The results show that the chemisorption energy depends weakly on the initial magnetization of the substrate and adsorbate, in agreement with recent experimental work done by Ertl's group. The magnetism of small metallic clusters was studied using the exact diagonalization procedure. The calculations, done for 5-site clusters, show a new interesting phenomenon involving spin frustration. The results indicate other many-body effects like the resonating valence bond state and singlet and triplet pairing. The many-body calculations were performed using various decoupling procedures, Gutzwiller variational schemes, and the connected-moment expansion. The performance of these techniques was tested and compared to exact results for small Hubbard clusters.
Many-body dipole-induced dipole model for electrorheological fluids
NASA Astrophysics Data System (ADS)
Huang, Ji-Ping; Yu, Kin-Wah
2004-07-01
Theoretical investigations on electrorheological (ER) fluids usually rely on computer simulations. An initial approach for these studies would be the point-dipole (PD) approximation, which is known to err considerably when the particles approach and finally touch each other due to many-body and multipolar interactions. Thus various works have attempted to go beyond the PD model. Being beyond the PD model, previous attempts have been restricted to either local-field effects only or multipolar effects only, but not both. For instance, we recently proposed a dipole-induced-dipole (DID) model which is shown to be both more accurate than the PD model and easy to use. This work is necessary because the many-body (local-field) effect is included to put forth the many-body DID model. The results show that the multipolar interactions can indeed be dominant over the dipole interaction, while the local-field effect may yield a correction.
Extended many-body potential of Hauschild and Prausnitz for pure HFD-like fluids
NASA Astrophysics Data System (ADS)
Abbaspour, Mohsen; Naderkhovy, Nasrin
2014-11-01
We have extended the many-body potential of Hauschild and Prausnitz (1993) in terms of the non-additivity coefficient and density (at different temperatures from liquid phase to supercritical region) for pure fluids. In order to compare our many-body potential with the accurate three-body potentials in the literature, we have performed molecular dynamics simulation to obtain pressure and self-diffusion coefficient values at different temperatures and densities using the two-body HFD-like potential and different three-body potentials. Our results indicated that our extended many-body potential is superior to the three-body potential of Guzman et al. (2011) for the different fluids and is also better than the three-body potential of Wang and Sadus (2006) for some noble gases.
Explicit Local Integrals of Motion for the Many-Body Localized State
NASA Astrophysics Data System (ADS)
Rademaker, Louk; OrtuÃ±o, 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.
Angle-resolved photoelectron spectra of metal cluster anions within a many-body-theory approach
NASA Astrophysics Data System (ADS)
Solov'Yov, Andrey V.; Polozkov, Roman G.; Ivanov, Vadim K.
2010-02-01
A consistent many-body theory based on the jellium model is applied for the description of angular resolved photoelectron spectra of metal clusters anions. The results of calculations demonstrate the dominant role of the many-body effects in the formation of angular distributions of photoelectrons emitted from sodium clusters and are in a good agreement with recent experimental data. The concrete comparison of theory and experiment has been performed for the photoionization of Na7- and Na19- anions being characterized by the entirely closed shells of delocalized electrons.
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.
Scheme of thinking quantum systems
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2009-11-01
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.
Charge optimized many-body (COMB) potential for dynamical simulation of Niâ€“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 Niâ€“Al system is presented within the third-generation charge optimized many-body (COMB3) formalism. The potential has been optimized for Ni3Al, or the Î³â€§ phase in Ni-based superalloys. The formation energies predicted for other Niâ€“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 (1â€‰1â€‰1) and (1â€‰0â€‰0) planes. It is also used to investigate dislocation propagation across the Ni3Al (1â€‰1â€‰0)â€“Ni (1â€‰1â€‰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 (1â€‰1â€‰1)â€“Al2O3 (0â€‰0â€‰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 mâ€‘2, which is in agreement with available experimental data. The predicted interlayer distance is further consistent with the available first-principles results for Ni (1â€‰1â€‰1)â€“Al2O3 (0â€‰0â€‰0â€‰1).
Charge optimized many-body (COMB) potential for dynamical simulation of Ni-Al phases.
Kumar, Aakash; Chernatynskiy, Aleksandr; Liang, Tao; Choudhary, Kamal; Noordhoek, Mark J; Cheng, Yu-Ting; Phillpot, Simon R; Sinnott, Susan B
2015-08-26
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 ?' 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). PMID:26234209
Complete fourth-order relativistic many-body calculations for atoms
Cannon, Caleb C.; Derevianko, Andrei
2004-03-01
We report, to our knowledge, the first relativistic calculation for many-electron atoms complete through the fourth order of many-body perturbation theory. Owing to an overwhelmingly large number of underlying diagrams, the calculations are aided by our suite of symbolic algebra tools. We augment all-order single-double excitation method with 1648 omitted fourth-order diagrams and compute amplitudes of principal transitions in Na. The resulting ab initio relativistic electric dipole amplitudes are in an excellent agreement with 0.05%-accurate experimental values. Analysis of previously unmanageable classes of diagrams provides a useful guide to a design of even more accurate, yet practical, many-body methods.
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.
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.
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.
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.
Photodetachment of metal cluster negative ions within many-body theory
NASA Astrophysics Data System (ADS)
Polozkov, R. G.; Ivanov, V. K.; Korol, A. V.; Solov'yov, A. V.
2012-11-01
The photodetachment cross section and photoelectron angular distribution of metal cluster negative ions are studied theoretically within the consistent many-body theory. Using the Hartree-Fock approximation for the delocalized electrons and the jellium model for the ionic core as the initial approximations, the many-electron correlations are taken into account within the Random Phase Approximation with Exchange. Our calculations demonstrate the dominant role of the many-body effects in the formation of cross sections and angular distributions of photoelectrons emitted from sodium clusters and are in good agreement with the existing experimental data. The concrete comparison of the theory and experiment has been performed for the photoionization of Na7 -, Na19 -, Na57 anions with entirely closed shells of delocalized electrons.
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 RÃ©nyi entropies are non-Gaussian. We find that RÃ©nyi entropies with different RÃ©nyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior.
A many-body term improves the accuracy of effective potentials based on protein coevolutionary data
NASA Astrophysics Data System (ADS)
Contini, A.; Tiana, G.
2015-07-01
The study of correlated mutations in alignments of homologous proteins proved to be successful not only in the prediction of their native conformation but also in the development of a two-body effective potential between pairs of amino acids. In the present work, we extend the effective potential, introducing a many-body term based on the same theoretical framework, making use of a principle of maximum entropy. The extended potential performs better than the two-body one in predicting the energetic effect of 308 mutations in 14 proteins (including membrane proteins). The average value of the parameters of the many-body term correlates with the degree of hydrophobicity of the corresponding residues, suggesting that this term partly reflects the effect of the solvent.
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.
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.
Detecting many-body entanglement in noninteracting ultracold atomic Fermi gases
Levine, G. C.; Bantegui, M. J.; Friedman, B. A.
2011-01-15
We explore the possibility of detecting many-body entanglement using time-of-flight (TOF) momentum correlations in ultracold atomic Fermi gases. In analogy to the vacuum correlations responsible for Bekenstein-Hawking black hole entropy, a partitioned atomic gas will exhibit particle-hole correlations responsible for entanglement entropy. The signature of these momentum correlations might be detected by a sensitive TOF-type experiment.
Theory of quantum coherence phenomena in semiconductor quantum dots.
Chow, Weng Wah; Phillips, Mark Christopher; Schneider, Hans Christian
2003-06-01
This paper explores quantum-coherence phenomena in a semiconductor quantum-dot structure. The calculations predict the occurrence of inversionless gain, electromagnetically induced transparency, and refractive-index enhancement in the transient regime for dephasing rates typical under room temperature and high excitation conditions. They also indicate deviations from atomic systems because of strong many-body effects. Specifically, Coulomb interaction involving states of the quantum dots and the continuum belonging to the surrounding quantum well leads to collision-induced population redistribution and many-body energy and field renormalizations that modify the magnitude, spectral shape, and time dependence of quantum-coherence effects.
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 coherence in multipartite systems
NASA Astrophysics Data System (ADS)
Yao, Yao; Xiao, Xing; Ge, Li; Sun, C. P.
2015-08-01
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord, and quantum entanglement in multipartite systems. On this basis, we define a basis-independent measure of quantum coherence and prove that it is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two-qubit unitary gates. Intriguingly, our results demonstrate that nonlocal unitary gates do not necessarily outperform the local unitary gates. Finally, the additivity relationship of quantum coherence in tripartite systems is discussed in detail, where the strong subadditivity of von Neumann entropy plays an essential role.
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
Protected quasilocality in quantum systems with long-range interactions
NASA Astrophysics Data System (ADS)
Cevolani, Lorenzo; Carleo, Giuseppe; Sanchez-Palencia, Laurent
2015-10-01
We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, interacting lattice bosons and spins are considered. Our study relies on a combined approach based on accurate many-body numerical calculations as well as on a quasiparticle microscopic theory. For sufficiently fast decaying long-range potentials, we find that the quantum speed limit set by the long-range Lieb-Robinson bounds is never attained and a purely ballistic behavior is found. For slowly decaying potentials, a radically different scenario is observed. In the bosonic case, a remarkable local spreading of correlations is still observed, despite the existence of infinitely fast traveling excitations in the system. This is in marked contrast to the spin case, where locality is broken. We finally provide a microscopic justification of the different regimes observed and of the origin of the protected locality in the bosonic model.
NASA Astrophysics Data System (ADS)
Caruso, Fabio; Atalla, Viktor; Ren, Xinguo; Rubio, Angel; Scheffler, Matthias; Rinke, Patrick
2014-08-01
We investigate charge transfer in prototypical molecular donor-acceptor compounds using hybrid density functional theory (DFT) and the GW approximation at the perturbative level (G0W0) and at full self-consistency (sc-GW). For the systems considered here, no charge transfer should be expected at large intermolecular separation according to photoemission experiments and accurate quantum-chemistry calculations. The capability of hybrid exchange-correlation functionals of reproducing this feature depends critically on the fraction of exact exchange ?, as for small values of ? spurious fractional charge transfer is observed between the donor and the acceptor. G0W0 based on hybrid DFT yields the correct alignment of the frontier orbitals for all values of ?. However, G0W0 has no capacity to alter the ground-state properties of the system because of its perturbative nature. The electron density in donor-acceptor compounds thus remains incorrect for small ? values. In sc-GW, where the Green's function is obtained from the iterative solution of the Dyson equation, the electron density is updated and reflects the correct description of the level alignment at the GW level, demonstrating the importance of self-consistent many-body approaches for the description of ground- and excited-state properties in donor-acceptor systems.
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.
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.
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.
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.
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.
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 and Kondo properties of cobalt-porphyrin molecules.
Reboredo, Fernando A; Tiago, Murilo L; Dagotto, Elbio R; Dias Da Silva, Luis G; Ulloa, Sergio E
2009-01-01
We use a unique combination of first principles many-body methods and the numerical renormalization-group technique to study the Kondo regime of cobalt-porphyrin compounds adsorbed on a Cu(111) surface. We find the Kondo temperature to be highly sensitive to both molecule charging and distance to the surface, which can explain the variations observed in recent scanning tunneling spectroscopy measurements. We discuss the importance of manybody effects in the molecular electronic structure controlling this phenomenon and suggest scenarios where enhanced temperatures can be achieved in experiments.
DPS Quantum Key Distribution System
NASA Astrophysics Data System (ADS)
Inoue, Kyo
Differential-phase-shift (DPS) quantum key distribution (QKD) is one scheme of quantum key distribution whose security is based on the quantum nature of lightwave. This protocol features simplicity, a high key creation rate, and robustness against photon-number-splitting attacks. We describe DPS-QKD in this paper, including its setup and operation, eavesdropping against DPS-QKD, system performance, and modified systems to improve the system performance.
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.
Relation of QCD sum rules in matter and the nuclear many-body problem
Shakin, C.M. )
1994-08-01
The method of QCD sum rules provides a powerful technique for the calculation of properties of hadrons in terms of a number of parameters that specify various condensate matrix elements. One may hope that it will be possible to calculate some of the condensate matrix elements using effective Lagrangians. If we concentrate on quark condensates, the Nambu--Jona-Lasinio model may provide a useful model. In this work we study the relation between relativistic nuclear many-body theory and the analysis of the nucleon self-energy in nuclear matter made using QCD sum rules. This is done by introducing the fields of a bosonized version of the Nambu--Jona-Lasinio (NJL) model. Using the simplest version of the QCD sum-rule analysis, we replace the QCD order parameters in matter with related order parameters describing a Lorentz scalar and a vector field. In our mean-field analysis we find that the many-body theory, based upon the bosonization of the NJL model, is consistent with the simplest version of the QCD sum-rule calculation of the nucleon self-energy in matter.
NASA Astrophysics Data System (ADS)
Rocca, Dario
2013-03-01
An accurate description of electronic excitations is essential to model and understand the properties of several materials of fundamental and technological interest. First principles, many-body techniques based on Green's functions are promising approaches that can provide an accurate description of excited state properties; however their applicability has long been hindered by their numerical complexity. In this talk we will summarize some recent methodological developments based on many-body perturbation theory for the efficient calculation of optical absorption spectra, photoemission spectra, and multiple exciton generation rates. Several applications to realistic materials will be presented, with emphasis on materials for solar energy applications; these include silicon nanowires and bulk tungsten oxide, that are promising photoelectrode materials in water splitting solar cells, molecules used in organic photovoltaics, and semiconductor nanoparticles with potential use in third generation photovoltaic cells based on multiple exciton generation. Work done in collaboration with Y. Ping, T. A. Pham, M. Voros, D. Lu, H.-V. Nguyen, S. Wippermann, A. Gali, G. T. Zimanyi, and G. Galli. *Present address Work supported by NSF-CHE-0802907.
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).
Experimental observation of spin-dependent electron many-body effects in CdTe
Horodyská, P.; N?mec, 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.
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 â„Î©D = 14 +/- 1 meV and an electron-phonon coupling strength of Î» = 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.
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 âˆ¼60 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)
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 Betheâ€“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 Kohnâ€“Sham energy gaps. In both cases quasiparticle band gaps are increased by up to 2â€‰eV, as compared to their Kohnâ€“Sham energy values. Inclusion of electronâ€“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.
Fidelity spectrum and phase transitions of quantum systems
Sacramento, P. D.; Vieira, V. R.; Paunkovic, N.
2011-12-15
Quantum fidelity between two density matrices F({rho}{sub 1},{rho}{sub 2}) is usually defined as the trace of the operator F={radical}({radical}({rho}{sub 1}){rho}{sub 2}{radical}({rho}{sub 1})). We study the logarithmic spectrum of this operator, which we denote by the fidelity spectrum, in the cases of the XX spin chain in a magnetic field, a magnetic impurity inserted in a conventional superconductor, and a bulk superconductor at finite temperature. When the density matrices are equal, {rho}{sub 1}={rho}{sub 2}, the fidelity spectrum reduces to the entanglement spectrum. We find that the fidelity spectrum can be a useful tool in giving a detailed characterization of the different phases of many-body quantum systems.
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.
Local controllability of quantum systems
NASA Astrophysics Data System (ADS)
Pucha?a, Zbigniew
2013-01-01
We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.
NASA Astrophysics Data System (ADS)
Deng, Haiming; Dai, Hui; Huang, Jiahao; Qin, Xizhou; Xu, Jun; Zhong, Honghua; He, Chunshan; Lee, Chaohong
2015-08-01
We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For an unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the interchain tunneling is much stronger than the intrachain one. The fractional insulator phases cannot be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the interchain bias. In the many-body Landau-Zener process, in which the interchain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011), 10.1038/nphys1801]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.
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.
Modified many-body wave function for BCS-BEC crossover in Fermi gases
Tan, Shina; Levin, K.
2006-10-15
We present a many-body formalism for BCS-BEC crossover, which represents a modification of the Bardeen-Cooper-Schrieffer-Leggett ground state to include four-fermion and higher correlations. In the Bose-Einstein condensate regime, we show how our approach contains the four-fermion behavior of Petrov et al. and associated scattering length a{sub dd} at short distances and, second, reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by a{sub dd}. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments, although one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Willow, Soohaeng Yoo; Zhang, Jinmei; Valeev, Edward F.; Hirata, So
2014-01-01
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 H2O, CH4, and C6H6 within a few mEh 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.
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.
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.
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.
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.
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.
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 Î“-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.
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 Î“-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
NASA Astrophysics Data System (ADS)
Barnes, Edwin; Hwang, E. H.; Throckmorton, R. E.; Das Sarma, S.
2014-06-01
Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order single-loop perturbative renormalization group (RG) analysis. Given that the effective (bare) coupling constant (i.e., the fine structure constant) in graphene is of order unity, which is neither small to justify a perturbative expansion nor large enough for strong-coupling theories to be applicable, the problem is a difficult one, with some similarity to (2+1)-dimensional strong-coupling quantum electrodynamics (QED). In this work, we take a systematic and comprehensive analytical approach in theoretically studying graphene many-body effects, primarily at the Dirac point (i.e., in undoped, intrinsic graphene), by going up to three loops in the diagrammatic expansion to both ascertain the validity of a perturbative expansion in the coupling constant and to develop a RG theory that can be used to estimate the actual quantitative renormalization effect to higher-order accuracy. Electron-electron interactions are expected to play an important role in intrinsic graphene due to the absence of screening at the Dirac (charge neutrality) point, potentially leading to strong deviations from the Fermi-liquid description around the charge neutrality point where the graphene Fermi velocity should manifest an ultraviolet logarithmic divergence because of the linear band dispersion. While no direct signatures for non-Fermi-liquid behavior at the Dirac point have yet been observed experimentally, there is ample evidence for the interaction-induced renormalization of the graphene velocity as the Dirac point is approached by lowering the carrier density. We provide a critical comparison between theory and experiment, using both higher-order diagrammatic and random phase approximation (i.e., infinite-order bubble diagrams) calculations, emphasizing future directions for a deeper understanding of the graphene effective field theory. We find that while the one-loop RG analysis gives reasonable quantitative agreement with the experimental data, both for graphene in vacuum and graphene on substrates, particularly when dynamical screening effects and finite carrier density effects are incorporated in the theory through the random phase approximation, the two-loop analysis reveals an interacting strong-coupling critical point in graphene suspended in vacuum signifying either a quantum phase transition or a breakdown of the weak-coupling renormalization group approach. By adapting a version of Dyson's argument for the breakdown of the QED perturbative expansion to the case of graphene, we show that in contrast to QED where the asymptotic perturbative series in the coupling constant converges to at least 137 orders (and possibly to much higher order) before diverging in higher orders, the graphene perturbative series in the coupling constant may manifest asymptotic divergence already in the first or second order in the coupling constant, favoring the conclusion that perturbation theory may be inadequate, particularly for graphene suspended in vacuum. We propose future experiments and theoretical directions to make further progress on this important and difficult problem. The question of convergence of the asymptotic perturbative expansion for graphene many-body effects is discussed critically in the context of the available experimental results and our theoretical calculations.
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; MÃ¸lmer, Klaus; Petrosyan, David; Rabl, Peter; Schmiedmayer, JÃ¶rg
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
Non-hermitian approach to decaying ultracold bosonic systems
NASA Astrophysics Data System (ADS)
Wimberger, Sandro; Parra-Murillo, Carlos A.; Kordas, Georgios
2013-06-01
A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures.
NASA Astrophysics Data System (ADS)
Blase, X.; Attaccalite, C.
2011-10-01
We study within the perturbative many-body GW (Green's function G and the screened Coulomb interaction W) and Bethe-Salpeter approach the low lying singlet charge-transfer excitations in molecular donor-acceptor complexes associating benzene, naphthalene, and anthracene derivatives with the tetracyanoethylene acceptor. Our calculations demonstrate that such techniques can reproduce the experimental data with a mean average error of 0.1-0.15 eV for the present set of dimers, in excellent agreement with the best time-dependent density functional studies with optimized range-separated functionals. The present results pave the way to the study of photoinduced charge transfer processes in photovoltaic devices with a parameter-free ab initio approach showing equivalent accuracy for finite and extended systems.
Quantum models of classical systems
NASA Astrophysics Data System (ADS)
Hájí?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.
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 ?-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)
Multiparticle-multihole configuration mixing description of nuclear many-body systems
Robin, C.; Pillet, N.; Le Bloas, J.; Berger, J.-F.
2014-10-15
In this work we discuss the multiparticle-multihole configuration mixing method which aims to describe the structure of atomic nuclei. Based on a variational principle it is able to treat in a unified way all types of long-range correlations between nucleons, without introducing symmetry breaking. The formalism is presented along with some preliminary results obtained for a few sd-shell nuclei. In the presented applications, the D1S Gogny force has been used.
Conditional pair distributions in many-body systems: exact results for Poisson ensembles.
Rohrmann, René D; Zurbriggen, Ernesto
2012-05-01
We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to within a certain distance of each other, with each of these two having a nearest neighbor to a fixed but otherwise arbitrary distance. This function describes special four-body configurations, but also contains contributions due to the so-called mutual nearest neighbor (two-body) and shared neighbor (three-body) configurations. The CPDF is introduced to improve a Helmholtz free energy method based on space partitions. We derive exact expressions of the CPDF and various associated quantities for randomly distributed, noninteracting points at Euclidean spaces of one, two, and three dimensions. Results may be of interest in many diverse scientific fields, from fluid physics to social and biological sciences. PMID:23004705
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.
Singular and fluctuational many body effects in the two-dimensional electron gas
NASA Astrophysics Data System (ADS)
Khalil, Iya G.
We investigate the role of many-body effects in the two-dimensional electron gas starting with the determination of the leading order corrections to the proper polarization. All three of the leading order diagrams exhibit singular logarithmic behavior in the derivative at momentum transfers q = 2kF and provide significant enhancement to the proper polarization particularly at low densities. Of particular importance is the contribution from the leading order fluctuational diagrams which exceed both the zeroth order (Lindhard) response and the self-energy and exchange contribution at a density of rs = 3. This is in contrast to the three-dimensional electron gas where the equivalent set of diagrams combined provide a much smaller enhancement to the three-dimensional zeroth order response than found in two-dimensions at an equivalent density. In addition, the fluctuational diagrams in three-dimensions contributed least in the metallic density range. These results therefore reinforce the notion that many-body effects are more significant in two-dimensions with importance placed on contributions arising from fluctuational effects. The local field factor formalism is employed to incorporate man-body effects to all orders in perturbation theory. We parameterize the local field factors in a strict manner that incorporates all known sum rules and exact limits. The local field factors then serve as essential input into the modified Kukkonen and Overhauser (KO) effective electron-electron interaction; here we find that spin fluctuations in the effective electron-electron interaction lead to additional attractive regions for triplet pairing near momentum transfers q = 2 kF. For singlet pairing, higher order manybody effects lead to a reduction in the attractive regions in the real part of the effective electron-electron interacting arising from plasmon exchange when compared to the effective electron-electron interaction in the random phase approximation. The KO effective electron-electron interaction serves as input into the frequency and momentum dependent Eliashberg equation where a preliminary solution of the Eliashberg equation indicates a favoring of intrinsic p-wave superconductivity at rs = 2.
Electron correlation: the many-body problem at the heart of chemistry.
Tew, David P; Klopper, Wim; Helgaker, Trygve
2007-06-01
The physical interactions among electrons and nuclei, responsible for the chemistry of atoms and molecules, is well described by quantum mechanics and chemistry is therefore fully described by the solutions of the Schrödinger equation. In all but the simplest systems we must be content with approximate solutions, the principal difficulty being the treatment of the correlation between the motions of the many electrons, arising from their mutual repulsion. This article aims to provide a clear understanding of the physical concept of electron correlation and the modern methods used for its approximation. Using helium as a simple case study and beginning with an uncorrelated orbital picture of electronic motion, we first introduce Fermi correlation, arising from the symmetry requirements of the exact wave function, and then consider the Coulomb correlation arising from the mutual Coulomb repulsion between the electrons. Finally, we briefly discuss the general treatment of electron correlation in modern electronic-structure theory, focussing on the Hartree-Fock and coupled-cluster methods and addressing static and dynamical Coulomb correlation. PMID:17269126
A many-body dissipative particle dynamics study of spontaneous capillary imbibition and drainage.
Chen, Chen; Gao, Chunning; Zhuang, Lin; Li, Xuefeng; Wu, Pingcang; Dong, Jinfeng; Lu, Juntao
2010-06-15
The spontaneous capillary imbibition and drainage processes are studied using many-body dissipative particle dynamics (MDPD) simulations. By adjusting the solid-liquid interaction parameter, different wetting behavior between the fluid and the capillary wall, corresponding to the static contact angle ranging from 0 degrees to 180 degrees, can be controllably simulated. For wetting fluids, the spontaneous capillary imbibition (SCI) is evident in MDPD simulations. It is found that, whereas the corrected Lucas-Washburn equation (taking into account the dynamic contact angle and the fluid inertia) can well describe the SCI simulation result for the completely wetting fluid, it deviates, to a notable degree, from the results of partly wetting fluids. In particular, this corrected equation cannot be used to describe the spontaneous capillary drainage (SCD) processes. To solve this problem, we derive an improved form of the Lucas-Washburn equation, in which the slip effects of fluid particles at the capillary wall are treated. Such an improved equation turns out to be capable of describing all the simulation results of both the SCI and the SCD. These findings provide new insights into the SCI and SCD processes and improve the mathematical base. PMID:20225880
Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions
Arienti, Marco; Pan, Wenxiao; Li, Xiaoyi; Karniadakis, George E.
2011-05-27
The combination of short-range repulsive and long-range attractive forces in Many-body Dissipative Particle Dynamics (MDPD) is examined at a vapor/liquid and liquid/solid interface. Based on the radial distribution of the virial pressure in a drop at equilibrium, a systematic study is carried out to characterize the sensitivity of the surface tension coefficient with respect to the inter-particle interaction parameters. For the first time, this study highlights the approximately cubic dependence of the surface tension coefficient on the bulk density of the fluid. In capillary flow, MDPD solutions are shown to satisfy the condition on the wavelength of an axial disturbance leading to the pinch-off of a cylindrical liquid thread. Correctly, no pinch-off occurs below the cutoff wavelength. MDPD is augmented by a set of bell-shaped weight functions to model interaction with a solid wall. There, hydrophilic and hydrophobic behaviors, including the occurrence of slip in the latter, are reproduced using a modification in the weight function that avoids particle clustering. Finally, the dynamics of droplets entering an inverted Y-shaped fracture junction is correctly captured in simulations parameterized by the Bond number, proving the flexibility of MDPD in modeling interface-dominated flows.
Effective many-body parameters for atoms in nonseparable Gaussian optical potentials
NASA Astrophysics Data System (ADS)
Wall, Michael L.; Hazzard, Kaden R. A.; Rey, Ana Maria
2015-07-01
We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and nonseparability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold-atom developments. We focus in particular on two potentials utilized in current ultracold-atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of nonseparability of eigenstates, borrowing ideas from the theory of matrix product states, leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.
Many-body effects in semiconducting single-wall silicon nanotubes
Wei, Wei
2014-01-01
Summary The electronic and optical properties of semiconducting silicon nanotubes (SiNTs) are studied by means of the many-body Green’s function method, i.e., GW approximation and Bethe–Salpeter equation. In these studied structures, i.e., (4,4), (6,6) and (10,0) SiNTs, self-energy effects are enhanced giving rise to large quasi-particle (QP) band gaps due to the confinement effect. The strong electron?electron (e?e) correlations broaden the band gaps of the studied SiNTs from 0.65, 0.28 and 0.05 eV at DFT level to 1.9, 1.22 and 0.79 eV at GW level. The Coulomb electron?hole (e?h) interactions significantly modify optical absorption properties obtained at noninteracting-particle level with the formation of bound excitons with considerable binding energies (of the order of 1 eV) assigned: the binding energies of the armchair (4,4), (6,6) and zigzag (10,0) SiNTs are 0.92, 1.1 and 0.6 eV, respectively. Results in this work are useful for understanding the physics and applications in silicon-based nanoscale device components. PMID:24455458
NASA Astrophysics Data System (ADS)
Leng, Xia; Yin, Huabing; Liang, Dongmei; Ma, Yuchen
2015-09-01
Organic semiconductors have promising and broad applications in optoelectronics. Understanding their electronic excited states is important to help us control their spectroscopic properties and performance of devices. There have been a large amount of experimental investigations on spectroscopies of organic semiconductors, but theoretical calculation from first principles on this respect is still limited. Here, we use density functional theory (DFT) and many-body Green's function theory, which includes the GW method and Bethe-Salpeter equation, to study the electronic excited-state properties and spectroscopies of one prototypical organic semiconductor, sexithiophene. The exciton energies of sexithiophene in both the gas and bulk crystalline phases are very sensitive to the exchange-correlation functionals used in DFT for ground-state structure relaxation. We investigated the influence of dynamical screening in the electron-hole interaction on exciton energies, which is found to be very pronounced for triplet excitons and has to be taken into account in first principles calculations. In the sexithiophene single crystal, the energy of the lowest triplet exciton is close to half the energy of the lowest singlet one. While lower-energy singlet and triplet excitons are intramolecular Frenkel excitons, higher-energy excitons are of intermolecular charge-transfer type. The calculated optical absorption spectra and Davydov splitting are in good agreement with experiments.
Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan; Pronobis, Wiktor; von Lilienfeld, O Anatole; Müller, Klaus-Robert; Tkatchenko, Alexandre
2015-06-18
Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the “holy grail” of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. In addition, the same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies. PMID:26113956
Leng, Xia; Yin, Huabing; Liang, Dongmei; Ma, Yuchen
2015-09-21
Organic semiconductors have promising and broad applications in optoelectronics. Understanding their electronic excited states is important to help us control their spectroscopic properties and performance of devices. There have been a large amount of experimental investigations on spectroscopies of organic semiconductors, but theoretical calculation from first principles on this respect is still limited. Here, we use density functional theory (DFT) and many-body Green's function theory, which includes the GW method and Bethe-Salpeter equation, to study the electronic excited-state properties and spectroscopies of one prototypical organic semiconductor, sexithiophene. The exciton energies of sexithiophene in both the gas and bulk crystalline phases are very sensitive to the exchange-correlation functionals used in DFT for ground-state structure relaxation. We investigated the influence of dynamical screening in the electron-hole interaction on exciton energies, which is found to be very pronounced for triplet excitons and has to be taken into account in first principles calculations. In the sexithiophene single crystal, the energy of the lowest triplet exciton is close to half the energy of the lowest singlet one. While lower-energy singlet and triplet excitons are intramolecular Frenkel excitons, higher-energy excitons are of intermolecular charge-transfer type. The calculated optical absorption spectra and Davydov splitting are in good agreement with experiments. PMID:26395713
Second-order many-body perturbation study on thermal expansion of solid carbon dioxide.
Li, Jinjin; Sode, Olaseni; Hirata, So
2015-01-13
An embedded-fragment ab initio second-order many-body perturbation (MP2) method is applied to an infinite three-dimensional crystal of carbon dioxide phase I (CO2-I), using the aug-cc-pVDZ and aug-cc-pVTZ basis sets, the latter in conjunction with a counterpoise correction for the basis-set superposition error. The equation of state, phonon frequencies, bulk modulus, heat capacity, Grüneisen parameter (including mode Grüneisen parameters for acoustic modes), thermal expansion coefficient (?), and thermal pressure coefficient (?) are computed. Of the factors that enter the expression of ?, MP2 reproduces the experimental values of the heat capacity, Grüneisen parameter, and molar volume accurately. However, it proves to be exceedingly difficult to determine the remaining factor, the bulk modulus (B0), the computed value of which deviates from the observed value by 50-100%. As a result, ? calculated by MP2 is systematically too low, while having the correct temperature dependence. The thermal pressure coefficient, ? = ?B0, which is independent of B0, is more accurately reproduced by theory up to 100 K. PMID:26574220
2015-01-01
Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the “holy grail” of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. In addition, the same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies. PMID:26113956
Thermal conductivity and energetic recoils in UO2 using a many-body potential model.
Qin, M J; Cooper, M W D; Kuo, E Y; Rushton, M J D; Grimes, R W; Lumpkin, G R; Middleburgh, S C
2014-12-10
Classical molecular dynamics simulations have been performed on uranium dioxide (UO2) employing a recently developed many-body potential model. Thermal conductivities are computed for a defect free UO2 lattice and a radiation-damaged, defect containing lattice at 300Â K, 1000Â K and 1500Â K. Defects significantly degrade the thermal conductivity of UO2 as does the presence of amorphous UO2, which has a largely temperature independent thermal conductivity of âˆ¼1.4Â Wm(-1)Â K(-1). The model yields a pre-melting superionic transition temperature at 2600Â K, very close to the experimental value and the mechanical melting temperature of 3600Â K, slightly lower than those generated with other empirical potentials. The average threshold displacement energy was calculated to be 37Â eV. Although the spatial extent of a 1Â keV U cascade is very similar to those generated with other empirical potentials and the number of Frenkel pairs generated is close to that from the Basak potential, the vacancy and interstitial cluster distribution is different. PMID:25398161