Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M.; Eric Tai, M.; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
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
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.
Entanglement dynamics in quantum many-body systems
NASA Astrophysics Data System (ADS)
Ho, Wen Wei; Abanin, Dmitry
The dynamics of quantum entanglement S (t) has proven useful to distinguishing different quantum many-body phases. In particular, the growth of entanglement following a quantum quench can be used to distinguish between many-body localized(S (t) ~ logt) and ergodic(S (t) ~ t) phases. Here, we provide a theoretical description of the growth of entanglement in a quantum many-body system, and propose a method to experimentally measure it. We show that entanglement growth is related to the spreading of local operators. In ergodic systems, the linear spreading of operators results in a universal, linear in time growth of entanglement. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of many copies of the original system, subject to a perturbation that reconnects different parts of the system. Using this picture, we propose an experimental set-up to measure entanglement growth by using a quantum switch (two-level system) which controls connections in the composite system. Our work provides a way to directly probe dynamical properties of many-body systems, in particular, allowing for a direct observation of many-body localization. This work was partially supported by Sloan Foundation, Ontario Early Researcher Award and NSERC Discovery Grant.
On microstates counting in many body polymer quantum systems
Chacon-Acosta, Guillermo; Morales-Tecotl, Hugo A.; Dagdug, Leonardo
2011-10-14
Polymer quantum systems are mechanical models quantized in a similar way as loop quantum gravity but in which loops/graphs resembling polymers are replaced by discrete sets of points. Such systems have allowed to study in a simpler context some novel aspects of loop quantum gravity. Although thermal aspects play a crucial role in cosmology and black hole physics little attention has been given to the thermostatistics of many body polymer quantum systems. In this work we explore how the features of a one-dimensional effective polymer gas, affect its microstate counting and hence the corresponding thermodynamical quantities.
Universal Behavior beyond Multifractality in Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Luitz, David J.; Alet, Fabien; Laflorencie, Nicolas
2014-02-01
How many states of a configuration space contribute to a wave function? Attempts to answer this ubiquitous question have a long history in physics and are keys to understanding, e.g., localization phenomena. Beyond single-particle physics, a quantitative study of the ground state complexity for interacting many-body quantum systems is notoriously difficult, mainly due to the exponential growth of the configuration (Hilbert) space with the number of particles. Here we develop quantum Monte Carlo schemes to overcome this issue, focusing on Shannon-Rényi entropies of ground states of large quantum many-body systems. Our simulations reveal a generic multifractal behavior while the very nature of quantum phases of matter and associated transitions is captured by universal subleading terms in these entropies.
Universal behavior beyond multifractality in quantum many-body systems.
Luitz, David J; Alet, Fabien; Laflorencie, Nicolas
2014-02-01
How many states of a configuration space contribute to a wave function? Attempts to answer this ubiquitous question have a long history in physics and are keys to understanding, e.g., localization phenomena. Beyond single-particle physics, a quantitative study of the ground state complexity for interacting many-body quantum systems is notoriously difficult, mainly due to the exponential growth of the configuration (Hilbert) space with the number of particles. Here we develop quantum Monte Carlo schemes to overcome this issue, focusing on Shannon-Rényi entropies of ground states of large quantum many-body systems. Our simulations reveal a generic multifractal behavior while the very nature of quantum phases of matter and associated transitions is captured by universal subleading terms in these entropies. PMID:24580627
Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Preiss, Philipp; Tai, Eric; Lukin, Alex; Schittko, Robert; Kaufman, Adam; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2016-05-01
The presence of large-scale entanglement is a defining characteristic of exotic quantum phases of matter. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. However, measuring entanglement remains a challenge. This is especially true 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. We demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. This protocol enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. In general, these experiments exemplify a method enabling the measurement and characterization of quantum phase transitions and in particular would be apt for studying systems such as magnetic ordering within the quantum Ising model.
Geodesic paths for quantum many-body systems
NASA Astrophysics Data System (ADS)
Tomka, Michael; Souza, Tiago; Rosenberg, Steve; Kolodrubetz, Michael; Polkovnikov, Anatoli
The quantum length is a distance between parameter-dependent eigenstates of an adiabatically driven quantum system. Its associated metric has many intriguing properties, for example it is related to the fidelity susceptibility, an important quantity in the study of quantum phase transitions. The metric also appears as the leading adiabatic correction of the energy fluctuations of a quantum system and gives rise to a time-energy uncertainty principle and a geometric interpretation of time. The adiabatic response of an open quantum system can as well be expressed through this metric. Further, the quantum length introduces the notion of Riemannian geometry to the manifold of eigenstates and hence allows one to define geodesics in parameter space. We study the geodesics in parameter space of certain quantum many-body systems, emerging from this quantum distance. These geodesic paths provide a well-defined optimal control protocol on how to drive the system's parameters in time, to get from one eigenstate to another. Generating optimal evolution plays a central role in quantum information technology, adiabatic quantum computing and quantum metrology. Swiss National Science Foundation (SNSF).
Dynamic Stabilization of a Quantum Many-Body Spin System
NASA Astrophysics Data System (ADS)
Hoang, T. M.; Gerving, C. S.; Land, B. J.; Anquez, M.; Hamley, C. D.; Chapman, M. S.
2013-08-01
We demonstrate dynamic stabilization of a strongly interacting quantum spin system realized in a spin-1 atomic Bose-Einstein condensate. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space, where subsequent free evolution gives rise to squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that rotate the spin-nematic many-body fluctuations and limit their growth. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is measured and compares well with a stability analysis.
Dynamic stabilization of a quantum many-body spin system.
Hoang, T M; Gerving, C S; Land, B J; Anquez, M; Hamley, C D; Chapman, M S
2013-08-30
We demonstrate dynamic stabilization of a strongly interacting quantum spin system realized in a spin-1 atomic Bose-Einstein condensate. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space, where subsequent free evolution gives rise to squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that rotate the spin-nematic many-body fluctuations and limit their growth. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is measured and compares well with a stability analysis. PMID:24033006
Boundary driven open quantum many-body systems
Prosen, Tomaž
2014-01-08
In this lecture course I outline a simple paradigm of non-eqjuilibrium quantum statistical physics, namely we shall study quantum lattice systems with local, Hamiltonian (conservative) interactions which are coupled to the environment via incoherent processes only at the system's boundaries. This is arguably the simplest nontrivial context where one can study far from equilibrium steady states and their transport properties. We shall formulate the problem in terms of a many-body Markovian master equation (the so-called Lindblad equation, and some of its extensions, e.g. the Redfield eqaution). The lecture course consists of two main parts: Firstly, and most extensively we shall present canonical Liouville-space many-body formalism, the so-called 'third quantization' and show how it can be implemented to solve bi-linear open many-particle problems, the key peradigmatic examples being the XY spin 1/2 chains or quasi-free bosonic (or harmonic) chains. Secondly, we shall outline several recent approaches on how to approach exactly solvable open quantum interacting many-body problems, such as anisotropic Heisenberg ((XXZ) spin chain or fermionic Hubbard chain.
Periodically driven ergodic and many-body localized quantum systems
Ponte, Pedro; Chandran, Anushya; Papić, Z.; Abanin, Dmitry A.
2015-02-15
We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.
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.
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
A perturbative probabilistic approach to quantum many-body systems
NASA Astrophysics Data System (ADS)
Di Stefano, Andrea; Ostilli, Massimo; Presilla, Carlo
2013-04-01
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the potential and hopping (amplitude and phase) values recorded during an infinitely lengthy evolution. We introduce a perturbative expansion of this probability distribution which conserves, at any order, a multinomial-like structure, typical of uncorrelated systems, but includes, order by order, the statistical correlations provided by the cumulant expansion. The proposed perturbative scheme is successfully tested in the case of pseudo-spin 1/2 hard-core boson Hubbard models also when affected by a phase problem due to an applied magnetic field.
Many-body localization in imperfectly isolated quantum systems.
Johri, Sonika; Nandkishore, Rahul; Bhatt, R N
2015-03-20
We use numerical exact diagonalization to analyze which aspects of the many-body localization phenomenon survive in an imperfectly isolated setting, when the system of interest is weakly coupled to a thermalizing environment. We show that widely used diagnostics (such as many-body level statistics and expectation values in exact eigenstates) cease to show signatures of many-body localization above a critical coupling that is exponentially small in the size of the environment. However, we also identify alternative diagnostics for many-body localization, in the spectral functions of local operators. Diagnostics include a discrete spectrum and a hierarchy of energy gaps, including a universal gap at zero frequency. These alternative diagnostics are shown to be robust, and continue to show signatures of many-body localization as long as the coupling to the bath is weaker than the characteristic energy scales in the system. We also examine how these signatures disappear when the coupling to the environment becomes larger than the characteristic energy scales of the system. PMID:25839306
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
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
Local shortcut to adiabaticity for quantum many-body systems
NASA Astrophysics Data System (ADS)
Mukherjee, Victor; Montangero, Simone; Fazio, Rosario
2016-06-01
We study the environmentally assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general the shortcut to adaiabaticity (STA) in quantum critical systems requires highly nonlocal control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use the transverse Ising model in one dimension to exemplify our generic results. We also extend our analysis to achieve LSTA in central spin models.
Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
NASA Astrophysics Data System (ADS)
Frérot, Irénée; Roscilde, Tommaso
2016-08-01
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed many-body quantum states remains a formidable challenge, with fundamental implications in areas as broad as quantum condensed matter, quantum information, quantum metrology, and quantum biology. Here, we provide a quantitative definition of the variance of quantum coherent fluctuations (the quantum variance) of any observable on generic quantum states. The quantum variance generalizes the concept of thermal de Broglie wavelength (for the position of a free quantum particle) to the space of eigenvalues of any observable, quantifying the degree of coherent delocalization in that space. The quantum variance is generically measurable and computable as the difference between the static fluctuations and the static susceptibility of the observable; despite its simplicity, it is found to provide a tight lower bound to most widely accepted estimators of "quantumness" of observables (both as a feature as well as a resource), such as the Wigner-Yanase skew information and the quantum Fisher information. When considering bipartite fluctuations in an extended quantum system, the quantum variance expresses genuine quantum correlations among the two parts. In the case of many-body systems, it is found to obey an area law at finite temperature, extending therefore area laws of entanglement and quantum fluctuations of pure states to the mixed-state context. Hence the quantum variance paves the way to the measurement of macroscopic quantum coherence and quantum correlations in most complex quantum systems.
Numerical approaches to isolated many-body quantum systems
NASA Astrophysics Data System (ADS)
Kolodrubetz, Michael H.
Ultracold atoms have revolutionized atomic and condensed matter physics. In addition to having clean, controllable Hamiltonians, ultracold atoms are near-perfect realizations of isolated quantum systems, in which weak environmental coupling can be neglected on experimental time scales. This opens new opportunities to explore these systems not just in thermal equilibrium, but out of equilibrium as well. In this dissertation, we investigate some properties of closed quantum systems, utilizing a combination of numerical and analytical techniques. We begin by applying full configuration-interaction quantum Monte Carlo (FCIQMC) to the Fermi polaron, which we use as a test bed to improve the algorithm. In addition to adapting standard QMC techniques, we introduce novel controlled approximations that allow mitigation of the sign problem and simulation directly in the thermodynamic limit. We also contrast the sign problem of FCIQMC with that of more standard techniques, focusing on FCIQMC's capacity to work in a second quantized determinant space. Next, we discuss nonequilibrium dynamics near a quantum critical point, focusing on the one-dimensional transverse-field Ising (TFI) chain. We show that the TFI dynamics exhibit critical scaling, within which the spin correlations exhibit qualitatively athermal behavior. We provide strong numerical evidence for the universality of dynamic scaling by utilizing time-dependent matrix product states to simulate a non-integrable model in the same equilibrium universality class. As this non-integrable model has been realized experimentally, we investigate the robustness of our predictions against the presence of open boundary conditions and disorder. We find that the qualitatively athermal correlations remain visible, although other phenomena such as even/odd effects become relevant within the finite size scaling theory. Finally, we investigate the properties of the integrable TFI model upon varying the strength of a non
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.
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.
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.
Theory of entropy production in quantum many-body systems
NASA Astrophysics Data System (ADS)
Solano-Carrillo, E.; Millis, A. J.
2016-06-01
We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second, and third laws of thermodynamics. For weakly coupled subsystems of an isolated system, an expression for the long-time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.
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
Quantum Fisher information as efficient entanglement witness in many-body systems
NASA Astrophysics Data System (ADS)
Hauke, Philipp
2016-05-01
Large-scale entanglement in quantum many-body systems is typically difficult to quantify experimentally. Here, we discuss scenarios where many-body entanglement becomes accessible via the quantum Fisher information (QFI), a known witness for genuinely multipartite entanglement as a resource for quantum-enhanced metrology. First, we introduce a direct relation of the QFI in thermal states with linear response functions, which makes the QFI measurable with standard methods in optical-lattice and solid-state experiments. Using this relationship, we show that close to continuous quantum phase transitions the QFI, and thus multipartite entanglement, is strongly divergent. Second, we demonstrate that the QFI can witness many-body localized phases, showing a characteristic growth of entanglement at long times after a quantum quench. These results demonstrate that the quantum Fisher information represents a useful and efficiently measurable witness for entanglement in quantum many-body settings.
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
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Werner, A. H.; Jaschke, D.; Silvi, P.; Kliesch, M.; Calarco, T.; Eisert, J.; Montangero, S.
2016-06-01
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems.
Werner, A H; Jaschke, D; Silvi, P; Kliesch, M; Calarco, T; Eisert, J; Montangero, S
2016-06-10
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies. PMID:27341253
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 physics—particularly the entanglement properties of a many-body system. This implies that it should be possible to measure many-body entanglement in relatively simple and tractable quantum systems. In addition, we studied charge relaxation in quantum RC circuits with a large number of conducting channels, and elucidated its relation to Kondo models in various regimes. We also extended our earlier work on the dynamics of driven and dissipative quantum spin-boson impurity systems, deriving a new formalism that makes it possible to compute the full spin density matrix and spin-spin correlation functions beyond the weak coupling limit. Finally, we provided a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in the case of a spinless dissipative resonant-level model. This project supported the research of two Ph.D. students and two postdoctoral researchers, whose training will allow them to further advance the field in coming years.
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
Quantum thermalization through entanglement in an isolated many-body system.
Kaufman, Adam M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Schittko, Robert; Preiss, Philipp M; Greiner, Markus
2016-08-19
Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis. PMID:27540168
Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems
Stimming, H.-P.; Mauser, N. J.; Mazets, I. E.
2010-07-02
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.
Equivalent dynamical complexity in a many-body quantum and collective human system
NASA Astrophysics Data System (ADS)
Johnson, Neil F.; Ashkenazi, Josef; Zhao, Zhenyuan; Quiroga, Luis
2011-03-01
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding of Fratini et al. concerning quantum many-body effects in cuprate superconductors (i.e. scale of 10-9 - 10-4 meters and 10-12 - 10-6 seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism (i.e. scale of 103 - 106 meters and 104 - 108 seconds), (iii) shows consistency with various established empirical facts for financial markets, neurons and human gangs and (iv) makes microscopic sense for each application. Our findings also suggest that a potentially productive shift can be made in Complexity research toward the identification of equivalent many-body dynamics in both classical and quantum regimes.
Thermopower as a tool to investigate many-body effects in quantum systems
Kristinsdóttir, L. H.; Bengtsson, J.; Reimann, S. M.; Wacker, A.; Linke, H.
2014-08-25
Measuring the thermopower of a confined quantum system reveals important information about its excitation spectrum. Our simulations show how this kind of transport spectroscopy is able to extract a clear signal for the onset of Wigner localization in a nanowire segment. This demonstrates that thermopower measurements provide a tool for investigating complex many-body quantum effects, which is less intrusive than the usual charge-stability diagram as no high source-drain bias is required. While the effect is most pronounced for weak tunnel coupling and low temperatures, the excited states also significantly affect the thermopower spectrum at moderate temperature, adding distinct features to the characteristic thermopower lineshape.
Single-shot simulations of dynamic quantum many-body systems
NASA Astrophysics Data System (ADS)
Sakmann, Kaspar; Kasevich, Mark
2016-05-01
Single experimental shots of ultracold quantum gases sample the many-particle probability distribution. In a few cases such single shots could be successfully simulated from a given many-body wavefunction, but for realistic time-dependent many-body dynamics this has been difficult to achieve. Here, we show how single shots can be simulated from numerical solutions of the time-dependent many-body Schrödinger equation. Using this approach, we provide first-principle explanations for fluctuations in the collision of attractive Bose-Einstein condensates (BECs), for the appearance of randomly fluctuating vortices and for the centre-of-mass fluctuations of attractive BECs in a harmonic trap. We also show how such simulations provide full counting distributions and correlation functions of any order. Such calculations have not been previously possible and our method is broadly applicable to many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.
NASA Astrophysics Data System (ADS)
Balz, Ben N.; Reimann, Peter
2016-06-01
We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably rare in time. Measuring the distinguishability in terms of quantum mechanical expectation values, results of this type have been previously established under increasingly weak assumptions about the initial disequilibrium, the many-body Hamiltonian, and the considered observables. Here, we further extend these results with respect to generalized distinguishability measures which fully take into account the fact that the actually observed, primary data are not expectation values but rather the probabilistic occurrence of different possible measurement outcomes.
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
Rahman Prize Talk: Pushing the frontier in the simulation of correlated quantum many body systems
NASA Astrophysics Data System (ADS)
Troyer, Matthias
Amazing progress in the simulation of correlated quantum many body systems has been achieved in the past two decades by combining significant advances in new algorithms with efficient implementations on ever faster supercomputers. This has enabled the accurate simulation of an increasing number of problems and helped settle many open questions. I will review a selection of results that my collaborators and I have worked on, from quantum phase transitions in quantum magnets, over supersolidity of bosons in lattice models and Helium-4 to recent simulations of correlated fermions and quantum gases. I will then provide an outlook to the future and discuss how in the short term analog quantum simulators can help tackle problems for which no efficient simulation algorithms exist and how in the longer term quantum computers can be used to solve many of the still open questions in the field. I will finally connect to the topic of the remainder of this symposium by touching on how the design of new topological materials will help in the construction of these quantum computers.
The Interplay of Localization and Interactions in Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Iyer, Shankar
systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting ("ergodic") phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
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.
Quantum phase transitions in the collective degrees of freedom: nuclei and other many-body systems
NASA Astrophysics Data System (ADS)
Cejnar, Pavel; Stránský, Pavel
2016-08-01
Quantum phase transitions (QPTs) represent a quickly developing subject of theoretical and experimental research. Nuclear physics contributed to the formation of the QPT concept in the 1970s and remains an area where new viewpoints and original approaches to criticality in many-body systems can be created. In this review, we present a comprehensible introduction to the subject, with an emphasis on the role of nuclear physics, and point out some specific features of QPTs in the systems that exhibit an effective separation of some collective degrees of freedom. The focus on collectivity, which stems from the nuclear context, is an essential ingredient of our treatise. It leads to some consequences that find application in nuclei as well as in a wide spectrum of non-nuclear systems.
Exploiting quantum parallelism to simulate quantum random many-body systems.
Paredes, B; Verstraete, F; Cirac, J I
2005-09-30
We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an auxiliary system. We show how our algorithm allows for the efficient simulation of dynamics of quantum random spin chains with known numerical methods. We propose an experimental realization based on atoms in optical lattices in which disorder could be simulated in parallel and in a controlled way through the interaction with another atomic species. PMID:16241634
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.
Quantum dynamical phase transition in a system with many-body interactions
NASA Astrophysics Data System (ADS)
Danieli, E. P.; Álvarez, G. A.; Levstein, P. R.; Pastawski, H. M.
2007-02-01
Recent experiments, [G.A. Álvarez, E.P. Danieli, P.R. Levstein, H.M. Pastawski, J. Chem. Phys. 124 (2006) 194507], have reported the observation of a quantum dynamical phase transition in the dynamics of a spin swapping gate. In order to explain this result from a microscopic perspective, we introduce a Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency ω0. For weak interactions with the environment 1/τ<2ω0, we find a slower oscillation whose amplitude decays with a rate 1/τϕ=1/(2τ). However, beyond a finite critical interaction with the environment, 1/τ>2ω0, the decay rate becomes 1/τϕ∝ω02τ. The oscillation period diverges showing a quantum dynamical phase transition to a Quantum Zeno phase consistent with the experimental observations.
Symmetry breaking and finite-size effects in quantum many-body systems
Koma, Tohru; Tasaki, Hal
1994-08-01
We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite-volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Neel order and the Hubbard model with a (superconducting) off-diagonal long-range order. In the corresponding finite system, the symmetry breaking is usually {open_quotes}obscured{close_quotes} by {open_quotes}quantum fluctuation{close_quotes} and one gets a symmetric ground state with a long-range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of order N{sup {minus}1}, where N denotes the number of sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we proved bounds for their energy expectation values. The bounds establish that there exist ever-increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant times N{sup {minus}1}. A crucial feature of the particular low-lying states we consider is that they can be regarded as finite-volume counterparts of this infinite-volume ground states. By forming linear combinations of these low-lying states and the (finite-volume) ground state and by taking infinite-volume limits, we construct infinite-volume ground states with explicit symmetry breaking. We conjecture that these infinite-volume ground states are ergodic, i.e., physically natural. Our general theorems not only shed light on the nature of symmetry breaking in quantum many-body systems, but also provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of interesting examples.
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.
Dynamics of isolated quantum systems: many-body localization and thermalization
NASA Astrophysics Data System (ADS)
Torres-Herrera, E. Jonathan; Tavora, Marco; Santos, Lea F.
2016-05-01
We show that the transition to a many-body localized phase and the onset of thermalization can be inferred from the analysis of the dynamics of isolated quantum systems taken out of equilibrium abruptly. The systems considered are described by one-dimensional spin-1/2 models with static random magnetic fields and by power-law band random matrices. We find that the short-time decay of the survival probability of the initial state is faster than exponential for sufficiently strong perturbations. This initial evolution does not depend on whether the system is integrable or chaotic, disordered or clean. At long-times, the dynamics necessarily slows down and shows a power-law behavior. The value of the power-law exponent indicates whether the system will reach thermal equilibrium or not. We present how the properties of the spectrum, structure of the initial state, and number of particles that interact simultaneously affect the value of the power-law exponent. We also compare the results for the survival probability with those for few-body observables. EJTH aknowledges financial support from PRODEP-SEP and VIEP-BUAP, Mexico.
Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System
NASA Astrophysics Data System (ADS)
Smith, Jacob; Senko, Crystal; Richerme, Phil; Lee, Aaron; Campbell, Wes; Monroe, Chris
2014-05-01
Trapped-ion quantum simulators are a promising candidate for exploring quantum-many-body physics, such as quantum magnetism, that are difficult to examine in condensed-matter experiments or using classical simulation. We demonstrate a coherent imaging spectroscopic technique to validate a quantum simulation. In this work, we study fully-connected transverse Ising models with a chain of up to 18 171Yb+ ions. Here, We resolve the state of each spin by collecting the spin-dependent fluorescence on a camera in order to map the complete energy spectrum and fully characterize the spin-spin couplings, while also engineering entangled states and measuring the critical gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators. This work is supported by grants from the U.S. Army Research Office with funding from the DARPA OLE program, IARPA, and the MURI program; and the NSF Physics Frontier Center at JQI.
Engl, Thomas; Dujardin, Julien; Argüelles, Arturo; Schlagheck, Peter; Richter, Klaus; Urbina, Juan Diego
2014-04-11
We predict a generic signature of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is robust with respect to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition principle in Fock space. It is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss their relevance in the context of many-body thermalization. PMID:24765925
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus
2015-05-01
Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.
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)
Deckman, Jason
The following dissertation is an account of my research in the Mandelshtam group at UC Irvine beginning in the Fall of 2006 and ending in the Summer of 2011. My general area of study falls within the realm of equilibrium quantum statistical mechanics, a discipline which attempts to relate molecular-scale properties to time averaged, macroscopic observables. The major tools used herein are the Variational Gaussian Wavepacket (VGW) approximation for quantum calculations, and Monte-Carlo methods, particularly parallel tempering, for global optimization and the prediction of equilibrium thermodynamic properties. Much of my work used these two methods to model both small and bulk systems at equilibrium where quantum effects are significant. All the systems considered are characterized by inter-molecular van der Waals forces, which are weak but significant electrostatic attractions between atoms and molecules and posses a 1/r6 dependence. The research herein begins at the microscopic level, starting with Lennard-Jones (LJ) clusters, then later shifts to the macroscopic for a study involving bulk para-hydrogen. For the LJ clusters the structural transitions induced by a changing deBoer parameter, Λ, a measure of quantum delocalization of the constituent particles, are investigated over a range of cluster sizes, N. From the data a "phase" diagram as a function of Λ and N is constructed, which depicts the structural motifs favored at different size and quantum parameter. Comparisons of the "quantum induced" structural transitions depicted in the latter are also made with temperature induced transitions and those caused by varying the range of the Morse potential. Following this, the structural properties of binary para-Hydrogen/ ortho-Deuterium clusters are investigated using the VGW approximation and Monte-Carlo methods within the GMIN framework. The latter uses the "Basin-Hopping" algorithm, which simplifies the potential energy landscape, and coupled with the VGW
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.
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.
Slow dynamics in many-body quantum systems with long range interactions
NASA Astrophysics Data System (ADS)
Santos, Lea; Perez-Bernal, Francisco
2016-05-01
In recent experiments with ion traps the range of the interactions between spins-1/2 can be controlled. In the limit of infinite-range interaction the system may be described by the Lipkin model, which exhibits an excited state quantum phase transition (ESQPT). The latter corresponds to a singularity in the spectrum that occurs at the ground state and propagates to higher energies as the control parameter increases beyond the ground state critical point. We show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, since the dynamics is usually expected to be very fast in systems with long-range interactions. This behavior is justified with the analysis of the structures of the eigenstates. This work was supported by the NSF Grant No. DMR-1147430.
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
NASA Astrophysics Data System (ADS)
Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco
2015-11-01
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Hernández-Rojas, Javier; Calvo, Florent; Noya, Eva Gonzalez
2015-03-10
The semiclassical method of quantum thermal baths by colored noise thermostats has been used to simulate various atomic systems in the molecular and bulk limits, at finite temperature and in moderately to strongly anharmonic regimes. In all cases, the method performs relatively well against alternative approaches in predicting correct energetic properties, including in the presence of phase changes, provided that vibrational delocalization is not too strong-neon appearing already as an upper limiting case. In contrast, the dynamical behavior inferred from global indicators such as the root-mean-square bond length fluctuation index or the vibrational spectrum reveals more marked differences caused by zero-point energy leakage, except in the case of isolated molecules with well separated vibrational modes. To correct for such deficiencies and reduce the undesired transfer among modes, empirical modifications of the noise power spectral density were attempted to better describe thermal equilibrium but still failed when used as semiclassical preparation for microcanonical trajectories. PMID:26579740
Short- and long-time dynamics of isolated many-body quantum systems
NASA Astrophysics Data System (ADS)
Tavora, Marco; Torres-Herrera, Jonathan; Ferreira Dos Santos, Lea
We show our results for the relaxation process of isolated interacting quantum spin chains in the integrable and chaotic regimes. The dynamics of the survival probability (the probability for finding the system still in its initial state at later times) and of few-body observables are analyzed. Different time scales are considered. While the short-time evolution is determined by the shape of the weighted energy distribution of the initial state, the long-time behavior depends on the bounds of the spectrum. Both numerical and analytical results are presented as well as comparisons with existing rigorous mathematical derivations. We consider initial states that can be prepared in experiments with cold atoms in optical lattices. Nsf Grant No. DMR-1147430.
Georgescu, Ionut; Deckman, Jason; Fredrickson, Laura J; Mandelshtam, Vladimir A
2011-05-01
A new method, here called thermal Gaussian molecular dynamics (TGMD), for simulating the dynamics of quantum many-body systems has recently been introduced [I. Georgescu and V. A. Mandelshtam, Phys. Rev. B 82, 094305 (2010)]. As in the centroid molecular dynamics (CMD), in TGMD the N-body quantum system is mapped to an N-body classical system. The associated both effective Hamiltonian and effective force are computed within the variational Gaussian wave-packet approximation. The TGMD is exact for the high-temperature limit, accurate for short times, and preserves the quantum canonical distribution. For a harmonic potential and any form of operator Â, it provides exact time correlation functions C(AB)(t) at least for the case of B, a linear combination of the position, x, and momentum, p, operators. While conceptually similar to CMD and other quantum molecular dynamics approaches, the great advantage of TGMD is its computational efficiency. We introduce the many-body implementation and demonstrate it on the benchmark problem of calculating the velocity time auto-correlation function for liquid para-hydrogen, using a system of up to N = 2592 particles. PMID:21548675
Controlling the Dynamics of an Open Many-Body Quantum System with Localized Dissipation
NASA Astrophysics Data System (ADS)
Barontini, G.; Labouvie, R.; Stubenrauch, F.; Vogler, A.; Guarrera, V.; Ott, H.
2013-01-01
We experimentally investigate the action of a localized dissipative potential on a macroscopic matter wave, which we implement by shining an electron beam on an atomic Bose-Einstein condensate (BEC). We measure the losses induced by the dissipative potential as a function of the dissipation strength observing a paradoxical behavior when the strength of the dissipation exceeds a critical limit: for an increase of the dissipation rate the number of atoms lost from the BEC becomes lower. We repeat the experiment for different parameters of the electron beam and we compare our results with a simple theoretical model, finding excellent agreement. By monitoring the dynamics induced by the dissipative defect we identify the mechanisms which are responsible for the observed paradoxical behavior. We finally demonstrate the link between our dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect. Because of the high degree of control on every parameter, our system is a promising candidate for the engineering of fully governable open quantum systems.
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems
NASA Astrophysics Data System (ADS)
Haegeman, Jutho; Van Acoleyen, Karel; Schuch, Norbert; Cirac, J. Ignacio; Verstraete, Frank
2015-01-01
We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS), we can show that an injective PEPS for the matter fields is gauged into a G -injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration-free gauge-theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge-invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z2 gauge theory with Higgs matter.
Berry's phase in a one-dimensional quantum many-body system
Schuetz, G. )
1994-03-01
We study an interacting one-dimensional quantum lattice gas of massive fermions on a ring with [ital L] lattice sites. The ring is threaded by a magnetic flux corresponding to a twist in boundary conditions. We compute the periodicity of the ground state under an adiabatically increasing flux and the associated Berry's phase occurring in this process. The model has a second-order phase transition line which coincides with a line where the Berry phase changes nonanalytically.
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.
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.
Quantum thermalization and many-body Anderson localization
NASA Astrophysics Data System (ADS)
Huse, David
2016-05-01
The out-of-equilibrium dynamics of closed quantum many-body systems can now be explored in a variety of laboratories using a variety of different physical systems, and as a consequence have received a lot of recent theoretical attention. When such systems do go to thermal equilibrium under their own unitary time evolution, this is what is called thermalization. Thermalization is what happens at long times in many large interacting and closed quantum systems, and one way of understanding part of how this happens is via the eigenstate thermalization hypothesis (ETH). The main generic exception to thermalization is many-body localization (MBL), where the system fails to act as a bath to thermalize itself, in spite of being strongly interacting. Instead, the quantum state of a MBL system remains localized near its initial state. MBL is now understood as a new type of quantum integrability, with localized conserved operators. There is a new type of quantum phase transition between MBL and thermalization as one decreases the static randomness in the system; this phase transition remains poorly understood.
Many-body localization in dipolar systems.
Yao, N Y; Laumann, C R; Gopalakrishnan, S; Knap, M; Müller, M; Demler, E A; Lukin, M D
2014-12-12
Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities. PMID:25541771
Quantum power functional theory for many-body dynamics
Schmidt, Matthias
2015-11-07
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.
Solving a quantum many-body problem by experiment
NASA Astrophysics Data System (ADS)
Schweigler, Thomas; Kasper, Valentin; Erne, Sebastian; Rauer, Bernhard; Langen, Tim; Gasenzer, Thomas; Berges, Jürgen; Schmiedmayer, Jörg
We experimentally study a pair of tunnel-coupled one-dimensional atomic superfluids, which realize the quantum sine-Gordon/massive Thirring models relevant for a wide variety of disciplines from particle to condensed-matter physics. From measured interference patterns we extract phase correlation functions and analyze if, and under which conditions, the higher-order correlation functions factorize into lower ones. This allows us to characterize the essential features of the model solely from our experimental measurements, detecting the relevant quasiparticles, their interactions and the topologically distinct vacua. Our method provides comprehensive insights into a non-trivial quantum field theory and establishes a general method to analyze quantum many-body systems through experiments. The method is also used to investigate the non-equilibrium dynamics following a quench in the tunnel-coupling between the superfluids.
Exploring flocking via quantum many-body physics techniques
NASA Astrophysics Data System (ADS)
Souslov, Anton; Loewe, Benjamin; Goldbart, Paul M.
2015-03-01
Flocking refers to the spontaneous breaking of spatial isotropy and time-reversal symmetries in collections of bodies such as birds, fish, locusts, bacteria, and artificial active systems. The transport of matter along biopolymers using molecular motors also involves the breaking of these symmetries, which in some cases are known to be broken explicitly. We study these classical nonequilibrium symmetry-breaking phenomena by means of models of many strongly interacting particles that hop on a periodic lattice. We employ a mapping between the classical and quantum dynamics of many-body systems, combined with tools from many-body theory. In particular, we examine the formation and properties of nematic and polar order in low-dimensional, strongly-interacting active systems using techniques familiar from fermionic systems, such as self-consistent field theory and bosonization. Thus, we find that classical active systems can exhibit analogs of quantum phenomena such as spin-orbit coupling, magnetism, and superconductivity. The models we study connect the physics of asymmetric exclusion processes to the spontaneous emergence of transport and flow, and also provide a soluble cousin of Vicsek's model system of self-propelled particles.
Collision Microscope to Study Many-Body Quantum Entanglement
NASA Astrophysics Data System (ADS)
Price, Craig; Liu, Qi; Gemelke, Nathan
2014-05-01
Quantum entanglement over long length scales is present in both quantum critical and quantum ordered many-body systems and can often be used as a fingerprint for underlying dynamics or ground-state structure. Limited quantum measurement and thermal back-action via controlled collisions of cold atoms and subsequent optical detection can be used to probe long-range entanglement. Entanglement Entropy has recently arisen as a quantitative vehicle to describe entanglement in thermodynamic systems, and its scaling with area can reveal detailed character of the system. We present progress in constructing an apparatus to experimentally extract Entanglement Entropy through pair-wise entanglement of cold fermionic potassium and bosonic cesium gases. The measurement will be made by translating localized probe atoms through a portion of a strongly entangled sample, then recording the heating effect of back-action after optical detection of probe atoms. To do so, precise independent control over the atoms will be maintained in a bichromatic lattice formed with a monolithic, common-mode optical setup imbedded in a quantum gas microscope. Other applications are discussed, including cooling of a Mott-Insulator and study of non-equilibrium quantum systems.
NASA Astrophysics Data System (ADS)
Santos, Lea F.; Távora, Marco; Pérez-Bernal, Francisco
2016-07-01
Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.
EDITORIAL: Focus on Quantum Information and Many-Body Theory
NASA Astrophysics Data System (ADS)
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac
Quantum quenches, thermalization, and many-body localization
NASA Astrophysics Data System (ADS)
Canovi, Elena; Rossini, Davide; Fazio, Rosario; Santoro, Giuseppe E.; Silva, Alessandro
2011-03-01
We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the system’s eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space.
On Many-Body Localization for Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-04-01
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
On Many-Body Localization for Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-06-01
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
EDITORIAL: Focus on Quantum Information and Many-Body Theory
NASA Astrophysics Data System (ADS)
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac
Using optical clock to probe quantum many-body physics
NASA Astrophysics Data System (ADS)
Ye, Jun
2016-05-01
The progress of optical lattice clock has benefited greatly from the understanding of atomic interactions. At the same time, the precision of clock spectroscopy has been applied to explore many-body spin interactions including SU(N) symmetry. Our recent work on this combined front of quantum metrology and many-body physics includes the probe of spin-orbital physics in the lattice clock and the investigation of a Fermi degenerate gas of 105 87Sr atoms in a three-dimensional magic-wavelength optical lattice.
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.
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
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 energy localization transition in periodically driven systems
D’Alessio, Luca; Polkovnikov, Anatoli
2013-06-15
According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space. -- Highlights: •A dynamical localization transition in periodically driven ergodic systems is found. •This phenomenon is reminiscent of many-body localization in energy space. •Our results are valid for classical and quantum systems in the thermodynamic limit. •At critical frequency, the short time expansion for the evolution operator breaks down. •The transition is associated to a divergent time scale.
A Many Body Eigenvalue Problem for Quantum Computation
NASA Astrophysics Data System (ADS)
Hershfield, Selman
2008-03-01
A one dimensional many body Hamiltonian is presented whose eigenvalues are related to the order of GN. This is the same order of GN used to decode the RSA algorithm. For some values of N the Hamiltonian is a noninteracting fermion problem. For other values of N the Hamiltonian is a quantum impurity problem with fermions interacting with a spin-like object. However, the generic case has fermions or spins interacting with higher order interactions beyond two body interactions. Because this is a mapping between two different classes of problems, one of interest in quantum computing and the other a more traditional condensed matter physics Hamiltonian, we will show (i) how knowledge of the order of GN can be used to solve some novel one dimensional strongly correlated problems and (ii) how numerical techniques, particularly for quantum impurity limit, can be used to find the order of GN.
Many-Body Effects in Quantum-Well Intersubband Transitions
NASA Technical Reports Server (NTRS)
Li, Jian-Zhong; Ning, Cun-Zheng
2003-01-01
Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (Qw) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons (ISPs). The oscillator strength of intersubband transitions (ISBTs) strongly varies with QW parameters and electron density because of this coupling. We have developed a set of kinetic equations, termed the intersubband semiconductor Bloch equations (ISBEs), from density matrix theory with the Hartree-Fock approximation, that enables a consistent description of these many-body effects. Using the ISBEs for a two-conduction-subband model, various many-body effects in intersubband transitions are studied in this work. We find interesting spectral changes of intersubband absorption coefficient due to interplay of the Fermi-edge singularity, subband renormalization, intersubband plasmon oscillation, and nonparabolicity of bandstructure. Our results uncover a new perspective for ISBTs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBT line shape.
NASA Astrophysics Data System (ADS)
Babadi, Mehrtash; Demler, Eugene; Knap, Michael
2015-10-01
We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-1 /2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1 /N expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild et al., Phys. Rev. Lett. 113, 147205 (2014), 10.1103/PhysRevLett.113.147205].
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.
Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
NASA Astrophysics Data System (ADS)
Vasseur, Romain; Moore, Joel E.
2016-06-01
We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.
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 energy localization transition in periodically driven system
NASA Astrophysics Data System (ADS)
D'Alessio, Luca; Polkovnikov, Anatoli
2013-03-01
According to the second law of thermodynamics the total entropy and energy of a system is increased during almost any dynamical process. 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. 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 periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space. We report numerical evidence based on exact diagonalization of small spin chains and theoretical arguments based on the Magnus expansion. Our findings are valid for both classical and quantum systems.
Typical fast thermalization processes in closed many-body systems
Reimann, Peter
2016-01-01
The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium. PMID:26926224
Ideal quantum glass transitions: Many-body localization without quenched disorder
Schiulaz, M.; Müller, M.
2014-08-20
We explore the possibility for translationally invariant quantum many-body systems to undergo a dynamical glass transition, at which ergodicity and translational invariance break down spontaneously, driven entirely by quantum effects. In contrast to analogous classical systems, where the existence of such an ideal glass transition remains a controversial issue, a genuine phase transition is predicted in the quantum regime. This ideal quantum glass transition can be regarded as a many-body localization transition due to self-generated disorder. Despite their lack of thermalization, these disorder-free quantum glasses do not possess an extensive set of local conserved operators, unlike what is conjectured for many-body localized systems with strong quenched disorder.
Entanglement between noncomplementary parts of many-body systems
NASA Astrophysics Data System (ADS)
Wichterich, H. C.
This thesis investigates the properties of entanglement in strongly correlated quantum systems, more specifically that between regions of a many-body system which may be separated spatially giving rise to a part of the system which is disregarded. The focus of the first part of this thesis is the response of a collection of spins, arranged on a one dimensional lattice, to a global quench, i.e. a rapid change in the interaction characteristics. Such a quench is seen to produce a significant amount of entanglement between distant spins. The robustness of the scheme towards random disorder is detailed and it is shown that the entanglement is sufficiently high to be distilled into almost pure Bell pairs. In a similar model system, it is explored how a von Neumann measurement with post-selection (i.e., discarding certain measurements based on the outcome) performed locally on two possibly well separated regions of spins, may give rise to a pure and entangled state of these regions, assuming the system is in its ground state. Later chapters are concerned with entanglement between noncomplementary groups of spins at quantum critical points, a situation where at zero temperature quantum fluctuations become pronounced. For spin chain models it is observed that this entanglement (as measured by negativity) assumes a finite value depending only on the ratio of the size of the regions to their separation and is further seen to be universal, i.e. independent of the microscopic details of the interaction. Universality of this form of entanglement is finally explored in a collective spin model. By casting the problem into the language of a few bosonic modes a closed form expression for the negativity in the thermodynamic limit for the entire phase diagram of the model is derived. At the quantum critical point this measure is explicitly universal in the aforementioned sense.
Exponentially Slow Heating in Periodically Driven Many-Body Systems
NASA Astrophysics Data System (ADS)
Abanin, Dmitry A.; De Roeck, Wojciech; Huveneers, François
2015-12-01
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.
NASA Astrophysics Data System (ADS)
Sohinger, Vedran
2015-11-01
In this paper, we will obtain a rigorous derivation of the defocusing cubic nonlinear Schr\\"{o}dinger equation on the three-dimensional torus $\\mathbb{T}^3$ from the many-body limit of interacting bosonic systems. This type of result was previously obtained on $\\mathbb{R}^3$ in the work of Erd\\H{o}s, Schlein, and Yau \\cite{ESY2,ESY3,ESY4,ESY5}, and on $\\mathbb{T}^2$ and $\\mathbb{R}^2$ in the work of Kirkpatrick, Schlein, and Staffilani \\cite{KSS}. Our proof relies on an unconditional uniqueness result for the Gross-Pitaevskii hierarchy at the level of regularity $\\alpha=1$, which is proved by using a modification of the techniques from the work of T. Chen, Hainzl, Pavlovi\\'{c} and Seiringer \\cite{ChHaPavSei} to the periodic setting. These techniques are based on the Quantum de Finetti theorem in the formulation of Ammari and Nier \\cite{AmmariNier1,AmmariNier2} and Lewin, Nam, and Rougerie \\cite{LewinNamRougerie}. In order to apply this approach in the periodic setting, we need to recall multilinear estimates obtained by Herr, Tataru, and Tzvetkov \\cite{HTT}. Having proved the unconditional uniqueness result at the level of regularity $\\alpha=1$, we will apply it in order to finish the derivation of the defocusing cubic nonlinear Schr\\"{o}dinger equation on $\\mathbb{T}^3$, which was started in the work of Elgart, Erd\\H{o}s, Schlein, and Yau \\cite{EESY}. In the latter work, the authors obtain all the steps of Spohn's strategy for the derivation of the NLS \\cite{Spohn}, except for the final step of uniqueness. Additional arguments are necessary to show that the objects constructed in \\cite{EESY} satisfy the assumptions of the unconditional uniqueness theorem. Once we achieve this, we are able to prove the derivation result. In particular, we show \\emph{Propagation of Chaos} for the defocusing Gross-Pitaevskii hierarchy on $\\mathbb{T}^3$ for suitably chosen initial data.
Coupling Identical one-dimensional Many-Body Localized Systems
NASA Astrophysics Data System (ADS)
Bordia, Pranjal; Lüschen, Henrik P.; Hodgman, Sean S.; Schreiber, Michael; Bloch, Immanuel; Schneider, Ulrich
2016-04-01
We experimentally study the effects of coupling one-dimensional many-body localized systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasirandom on-site disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between many-body localization and Anderson localization. While the noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system.
Quantum lattice-gas models for the many-body schroedinger equation
Boghosian, B.M.; Taylor, W. IV
1997-08-01
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schroedinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schroedinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.
Phase transitions in fermionic systems with many-body interaction
NASA Technical Reports Server (NTRS)
Bozzolo, G.; Plastino, A.; Ferrante, J.
1989-01-01
A linearized version of the Hartree-Fock method is used as a probe to investigate phase transitions in fermionic systems with many-body interactions. An application to a new exactly solvable model which includes two- and three-body forces is shown.
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.
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.
Ponte, Pedro; Papić, Z; Huveneers, François; Abanin, Dmitry A
2015-04-10
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases. PMID:25910094
Theory of many-body localization in periodically driven systems
NASA Astrophysics Data System (ADS)
Abanin, Dmitry A.; De Roeck, Wojciech; Huveneers, François
2016-09-01
We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau-Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.
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.
Porter-Thomas distribution in unstable many-body systems
Volya, Alexander
2011-04-15
We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and the collectivity that emerges in nonstationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between the structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.
Quantum Measurement of Spin Correlations in a Symmetric Many-Body State ∖ f 1
NASA Astrophysics Data System (ADS)
Shojaee, Ezad; Kalev, Amir; Deutsch, Ivan; Cquic Team
2016-05-01
Continuous (nonprojective) measurement on a quantum system has been employed previously for fast, robust, and high-fidelity quantum state tomography (QST) on qudits. We expand this protocol to many-body systems in order to perform QST on the reduced one-body and two-body density matrices of a symmetric many-body state of multiple qubits. Such QST will characterize the spin correlations in the system. In this protocol, a continuous measurement is done collectively on many copies of the reduced state at the same time, and therefore, while it is weakly perturbative on each copy, yields high signal-to-noise. Simultaneously, we subject the system to an external collective control in order to generate an informationally complete measurement record. We characterize the information-gain measurement disturbance tradeoff in terms of parameters in the problem (number of qubits, control parameters, shot-noise bandwidth, and the measurement strength). Support from NSF is acknowledged.
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.
Simulation of the many-body dynamical quantum Hall effect in an optical lattice
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Yang, Xu-Chen
2016-05-01
We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations.
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 dynamics of a Bose system with attractive interactions on a ring
Li Weibin; Xie Xiaotao; Yang Xiaoxue; Zhan Zhiming
2005-10-15
We investigate the many-body dynamics of an effectively attractive one-dimensional Bose system confined in a toroidal trap. The mean-field theory predicts that a bright-soliton state will be formed when the interparticle interaction increases over a critical point. The study of quantum many-body dynamics in this paper reveals that there is a modulation instability in a finite Bose system correspondingly. We show that Shannon entropy becomes irregular near and above the critical point due to quantum correlations. We also study the dynamical behavior of the instability by exploring the momentum distribution and the fringe visibility, which can be verified experimentally by releasing the trap.
Spectral statistics of chaotic many-body systems
NASA Astrophysics Data System (ADS)
Dubertrand, Rémy; Müller, Sebastian
2016-03-01
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross-Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose-Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner-Dyson ensembles of random matrix theory. The conditions for Wigner-Dyson statistics involve a gap in the spectrum of the Frobenius-Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.
Dynamics of many-body localization in a translation-invariant quantum glass model
NASA Astrophysics Data System (ADS)
van Horssen, Merlijn; Levi, Emanuele; Garrahan, Juan P.
2015-09-01
We study the real-time dynamics of a translationally invariant quantum spin chain, based on the East kinetically constrained glass model, in search for evidence of many-body localization in the absence of disorder. Numerical simulations indicate a change, controlled by a coupling parameter, from a regime of fast relaxation-corresponding to thermalization-to a regime of very slow relaxation. This slowly relaxing regime is characterized by dynamical features usually associated with nonergodicity and many-body localization (MBL): memory of initial conditions, logarithmic growth of entanglement entropy, and nonexponential decay of time correlators. We show that slow relaxation is a consequence of sensitivity to spatial fluctuations in the initial state. While numerical results and physical considerations indicate that relaxation time scales grow markedly with size, our finite size results are consistent both with an MBL transition, expected to only occur in disordered systems, and with a pronounced quasi-MBL crossover.
Experimental quantum simulations of many-body physics with trapped ions.
Schneider, Ch; Porras, Diego; Schaetz, Tobias
2012-02-01
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems. PMID:22790343
Digital quantum simulation of many-body non-Markovian dynamics
NASA Astrophysics Data System (ADS)
Sweke, R.; Sanz, M.; Sinayskiy, I.; Petruccione, F.; Solano, E.
2016-08-01
We present an algorithmic method for the digital quantum simulation of many-body locally indivisible non-Markovian open quantum systems. It consists of two parts: first, a Suzuki-Lie-Trotter decomposition of the global system propagator into the product of subsystem propagators, which may not be quantum channels, and second, an algorithmic procedure for the implementation of the subsystem propagators through unitary operations and measurements on a dilated space. By providing rigorous error bounds for the relevant Suzuki-Lie-Trotter decomposition, we are able to analyze the efficiency of the method, and connect it with an appropriate measure of the local indivisibility of the system. In light of our analysis, the proposed method is expected to be experimentally achievable for a variety of interesting cases.
Fisher entropy and uncertaintylike relationships in many-body systems
NASA Astrophysics Data System (ADS)
Romera, E.; Angulo, J. C.; Dehesa, J. S.
1999-05-01
General model-independent relationships among radial expectation values of the one-particle densities in position and momentum spaces for any quantum-mechanical system are obtained. They are derived from the Stam uncertainty principle and the recently reported lower bounds to the Fisher information entropy of both densities. The results are usually expressed in terms of some uncertainty products of the system. The accuracy of the bounds is numerically analyzed for neutral atoms within a Hartree-Fock framework.
Quantum many-body dynamics in a Lagrangian frame: I. Equations of motion and conservation laws
NASA Astrophysics Data System (ADS)
Tokatly, I. V.
2005-04-01
We formulate equations of motion and conservation laws for a quantum many-body system in a co-moving Lagrangian reference frame. It is shown that generalized inertia forces in the co-moving frame are described by Green’s deformation tensor gμν(ξ,t) and a skew-symmetric vorticity tensor Ftilde μν(ξ,t) , where ξ in the Lagrangian coordinate. Equations of motion are equivalent to those for a quantum many-body system in a space with time-dependent metric gμν(ξ,t) in the presence of an effective magnetic field Ftilde μν(ξ,t) . To illustrate the general formalism we apply it to the proof of the harmonic potential theorem. As another example of application we consider a fast long wavelength dynamics of a Fermi system in the dynamic Hartree approximation. In this case the kinetic equation in the Lagrangian frame can be solved explicitly. This allows us to formulate the description of a Fermi gas in terms of an effective nonlinear elasticity theory. We also discuss a relation of our results to time-dependent density functional theory.
Off-resonant many-body quantum carpets in strongly tilted optical lattices
NASA Astrophysics Data System (ADS)
Muñoz-Arias, Manuel H.; Madroñero, Javier; Parra-Murillo, Carlos A.
2016-04-01
A unit filling Bose-Hubbard Hamiltonian embedded in a strong Stark field is studied in the off-resonant regime inhibiting single- and many-particle first-order tunneling resonances. We investigate the occurrence of coherent dipole wavelike propagation along an optical lattice by means of an effective Hamiltonian accounting for second-order tunneling processes. It is shown that dipole wave function evolution in the short-time limit is ballistic and that finite-size effects induce dynamical self-interference patterns known as quantum carpets. We also present the effects of the border right after the first reflection, showing that the wave function diffuses normally with the variance changing linearly in time. This work extends the rich physical phenomenology of tilted one-dimensional lattice systems in a scenario of many interacting quantum particles, the so-called many-body Wannier-Stark system.
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 α-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
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
2012-08-21
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 α-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
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.
Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-07-01
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a Kolmogorov-Arnold-Moser-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor-product basis into a complete set of exact many-body eigenfunctions.
Engineering many-body dynamics with quantum light potentials and measurements
NASA Astrophysics Data System (ADS)
Elliott, T. J.; Mekhov, I. B.
2016-07-01
Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterize these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunable effects such as long-range density-density interactions, perfectly correlated atomic tunneling, superexchange, and effective pair processes. We further show that this provides a framework for enhancing quantum simulations to include such long-range and correlated processes, including reservoir models and dynamical global gauge fields.
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.
The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations
Sellier, J.M. Dimov, I.
2014-09-15
The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.
Terahertz quantum well photodetectors with improved designs by exploiting many-body effects
NASA Astrophysics Data System (ADS)
Ferré, Simon; Razavipour, Seyed Ghasem; Ban, Dayan
2013-08-01
A systematic study on many-body effects on Terahertz Quantum Well Photodetectors (THZ QWPs) is reported. Peak absorption frequency differs by more than 20% when taking many-body effects into account. The phenomenon is shown to be critical in designs with a small barrier height and a high doping density. In order to exploit them and minimize their adverse impacts, a doping profile symmetrically split in the barrier layers, resembling a double-barrier QWP, is proposed. Simulation results show the design reduces dark current by one order of magnitude compared against conventional designs with a uniform doping profile in the quantum well.
Exploring Quantum Many-Body Spin Dynamics with Truncated Wigner Methods
NASA Astrophysics Data System (ADS)
Schachenmayer, Johannes
Recent experiments in atomic, molecular, and optical physics offer controlled and clean environments to experimentally study non-equilibrium dynamics of large many-body quantum spin-models with variable range interactions. Thus, efficient computation of such dynamics is of great importance. While in one dimension, time-dependent density matrix renormalization group methods (t-DMRG) have proven effective under certain conditions, computing dynamics in higher dimensional systems remains an outstanding challenge. Recently we formulated the discrete truncated Wigner approximation (DTWA), a semiclassical method based on the truncated Wigner approximation (TWA) that has been proven to be surprisingly accurate in predicting quench dynamics in high-dimensional lattices with up to tens of thousands of quantum spins. Here, we introduce the DTWA and show how it can compute time-evolution of quantum states in experiments that engineer spin-models with polar molecules in optical lattices or with ions in two-dimensional Penning traps. We show, how the DTWA can provide results for the time-evolution of classical and quantum correlations in quench experiments in regimes where other numerical methods are generally unreliable. We report on progress of how to incorporate higher order corrections to the method, and how to adapt it to systems with both spin and bosonic degrees of freedom.
Nonperturbative THz nonlinearities for many-body quantum control in semiconductors
NASA Astrophysics Data System (ADS)
Lange, C.; Maag, T.; Bayer, A.; Hohenleutner, M.; Baierl, S.; Bougeard, D.; Mootz, M.; Koch, S. W.; Kira, M.; Huber, R.
2016-03-01
Quantum computing and ultrafast quantum electronics constitute pivotal technologies of the 21st century and revolutionize the way we process information. Successful implementations require controlling superpositions of states and coherence in matter, and exploit nonlinear effects for elementary logic operations. In the THz frequency range between optics and electronics, solid state systems offer a rich spectrum of collective excitations such as excitons, phonons, magnons, or Landau electrons. Here, single-cycle THz transients of 8.7 kV/cm amplitude centered at 1 THz strongly excite inter-Landau-level transitions of magnetically biased GaAs quantum wells, facilitating coherent Landau ladder climbing by more than six rungs, population inversion, and coherent polarization control. Strong, highly nonlinear pump-probe and four- and six-wave mixing signals, entirely unexpected for this paragon of the harmonic oscillator, are revealed through two-time THz spectroscopy. In this scenario of nonperturbative polarization dynamics, our microscopic theory shows how the protective limits of Kohn's theorem are ultimately surpassed by dynamically enhanced Coulomb interactions, opening the door to exploiting many-body dynamics for nonlinear quantum control.
The nonequilibrium quantum many-body problem as a paradigm for extreme data science
NASA Astrophysics Data System (ADS)
Freericks, J. K.; Nikolić, B. K.; Frieder, O.
2014-12-01
Generating big data pervades much of physics. But some problems, which we call extreme data problems, are too large to be treated within big data science. The nonequilibrium quantum many-body problem on a lattice is just such a problem, where the Hilbert space grows exponentially with system size and rapidly becomes too large to fit on any computer (and can be effectively thought of as an infinite-sized data set). Nevertheless, much progress has been made with computational methods on this problem, which serve as a paradigm for how one can approach and attack extreme data problems. In addition, viewing these physics problems from a computer-science perspective leads to new approaches that can be tried to solve more accurately and for longer times. We review a number of these different ideas here.
Many-Body Effect in Spin Dephasing in n-Type GaAs Quantum Wells
NASA Astrophysics Data System (ADS)
Weng, Ming-Qi; Wu, Ming-Wei
2005-03-01
By constructing and numerically solving the kinetic Bloch equations we perform a many-body study of the spin dephasing due to the D'yakonov-Perel' effect in n-type GaAs (100) quantum wells for high temperatures. In our study, we include the spin-conserving scattering such as the electron-phonon, the electron-nonmagnetic impurity as well as the electron-electron Coulomb scattering into consideration. The dephasing obtained from our theory contains both the single-particle and the many-body contributions with the latter originating from the inhomogeneous broadening introduced by the DP term [J. Supercond.: Incorp. Novel Magn. 14 (2001) 245 Eur. Phys. J. B 18 (2000) 373]. Our result agrees very well with the experimental data [Phys. Rev. B 62 (2000) 13034] of Malinowski et al. We further show that in the case we study, the spin dephasing is dominated by the many-body effect.
Dynamics of a Many-Body-Localized System Coupled to a Bath.
Fischer, Mark H; Maksymenko, Mykola; Altman, Ehud
2016-04-22
Coupling a many-body-localized system to a dissipative bath necessarily leads to delocalization. Here, we investigate the nature of the ensuing relaxation dynamics and the information it holds on the many-body-localized state. We formulate the relevant Lindblad equation in terms of the local integrals of motion of the underlying localized Hamiltonian. This allows us to map the quantum evolution deep in the localized state to tractable classical rate equations. We consider two different types of dissipation relevant to systems of ultracold atoms: dephasing due to inelastic scattering on the lattice lasers and particle loss. Our approach allows us to characterize their different effects in the limiting cases of weak and strong interactions. PMID:27152775
Dynamics of a Many-Body-Localized System Coupled to a Bath
NASA Astrophysics Data System (ADS)
Fischer, Mark H.; Maksymenko, Mykola; Altman, Ehud
2016-04-01
Coupling a many-body-localized system to a dissipative bath necessarily leads to delocalization. Here, we investigate the nature of the ensuing relaxation dynamics and the information it holds on the many-body-localized state. We formulate the relevant Lindblad equation in terms of the local integrals of motion of the underlying localized Hamiltonian. This allows us to map the quantum evolution deep in the localized state to tractable classical rate equations. We consider two different types of dissipation relevant to systems of ultracold atoms: dephasing due to inelastic scattering on the lattice lasers and particle loss. Our approach allows us to characterize their different effects in the limiting cases of weak and strong interactions.
Algorithm for simulation of quantum many-body dynamics using dynamical coarse-graining
NASA Astrophysics Data System (ADS)
Khasin, M.; Kosloff, R.
2010-04-01
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 n3/2(lnn)-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 2×104 and 2×106 cold atoms in a double-well trap, described by the two-site Bose-Hubbard model.
Dynamic correlations in Brownian many-body systems.
Brader, Joseph M; Schmidt, Matthias
2014-01-21
For classical Brownian systems driven out of equilibrium, we derive inhomogeneous two-time correlation functions from functional differentiation of the one-body density and current with respect to external fields. In order to allow for appropriate freedom upon building the derivatives, we formally supplement the Smoluchowski dynamics by a source term, which vanishes at the physical solution. These techniques are applied to obtain a complete set of dynamic Ornstein-Zernike equations, which serve for the development of approximation schemes. The rules of functional calculus lead naturally to non-Markovian equations of motion for the two-time correlators. Memory functions are identified as functional derivatives of a unique space- and time-nonlocal dissipation power functional. PMID:25669360
Area laws and efficient descriptions of quantum many-body states
NASA Astrophysics Data System (ADS)
Ge, Yimin; Eisert, Jens
2016-08-01
It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states—a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this work, we show that this is in general not the case, except in one-dimension. We prove that the set of quantum many-body states that satisfy an area law for all Renyi entropies contains a subspace of exponential dimension. We then show that there are states satisfying area laws for all Renyi entropies but cannot be approximated by states with a classical description of small Kolmogorov complexity, including polynomial projected entangled pair states or states of multi-scale entanglement renormalisation. Not even a quantum computer with post-selection can efficiently prepare all quantum states fulfilling an area law, and we show that not all area law states can be eigenstates of local Hamiltonians. We also prove translationally and rotationally invariant instances of these results, and show a variation with decaying correlations using quantum error-correcting codes.
Blocking transport resonances via Kondo many-body entanglement in quantum dots
Niklas, Michael; Smirnov, Sergey; Mantelli, Davide; Margańska, Magdalena; Nguyen, Ngoc-Viet; Wernsdorfer, Wolfgang; Cleuziou, Jean-Pierre; Grifoni, Milena
2016-01-01
Many-body entanglement is at the heart of the Kondo effect, which has its hallmark in quantum dots as a zero-bias conductance peak at low temperatures. It signals the emergence of a conducting singlet state formed by a localized dot degree of freedom and conduction electrons. Carbon nanotubes offer the possibility to study the emergence of the Kondo entanglement by tuning many-body correlations with a gate voltage. Here we show another side of Kondo correlations, which counterintuitively tend to block conduction channels: inelastic co-tunnelling lines in the magnetospectrum of a carbon nanotube strikingly disappear when tuning the gate voltage. Considering the global SU(2) ⊗ SU(2) symmetry of a nanotube coupled to leads, we find that only resonances involving flips of the Kramers pseudospins, associated to this symmetry, are observed at temperatures and voltages below the corresponding Kondo scale. Our results demonstrate the robust formation of entangled many-body states with no net pseudospin. PMID:27526870
Blocking transport resonances via Kondo many-body entanglement in quantum dots.
Niklas, Michael; Smirnov, Sergey; Mantelli, Davide; Margańska, Magdalena; Nguyen, Ngoc-Viet; Wernsdorfer, Wolfgang; Cleuziou, Jean-Pierre; Grifoni, Milena
2016-01-01
Many-body entanglement is at the heart of the Kondo effect, which has its hallmark in quantum dots as a zero-bias conductance peak at low temperatures. It signals the emergence of a conducting singlet state formed by a localized dot degree of freedom and conduction electrons. Carbon nanotubes offer the possibility to study the emergence of the Kondo entanglement by tuning many-body correlations with a gate voltage. Here we show another side of Kondo correlations, which counterintuitively tend to block conduction channels: inelastic co-tunnelling lines in the magnetospectrum of a carbon nanotube strikingly disappear when tuning the gate voltage. Considering the global SU(2) ⊗ SU(2) symmetry of a nanotube coupled to leads, we find that only resonances involving flips of the Kramers pseudospins, associated to this symmetry, are observed at temperatures and voltages below the corresponding Kondo scale. Our results demonstrate the robust formation of entangled many-body states with no net pseudospin. PMID:27526870
INTRODUCTION: Many-Body Theory of Atomic Systems: Proceedings of the Nobel Symposium 46
NASA Astrophysics Data System (ADS)
Lindgren, Ingvar; Lundqvist, Stig
1980-01-01
corresponding experimental results, which will eventually lead to a better understanding of the behaviour of many-electron systems and possibly also of many-fermion systems in general. In addition to the static properties of atomic systems there is nowadays a great interest in the dynamics of the excitation process, which is of fundamental importance for our understanding of photoelectron and photoabsorption spectra. The experimental data being produced in this field are enormous and many intricate physical problems appear, which can only be understood by considering the atom as a fully interacting many-body system. All the new developments mentioned here have opened entirely new areas in atomic many-body theory, and we are evidently just at the verge of a very interesting period of rapid progress. It is quite evident that we could have limited the Symposium to atomic problems of the type described here. However, related problems appear in atoms bound in solids and in atoms/molecules bound to solid surfaces. Therefore, we proposed to include also some aspects of these fields in our program, which brought together scientists with different backgrounds, such as atomic and molecular physicists, theoretical chemists, solid state and surface physicists as well as nuclear physicists and quantum- liquid experts. The Symposium then got a distinctive inter-disciplinary character at the same time as it was concentrated on the specific atomic many-body problem. The response to our invitations to the Nobel Symposium was overwhelming. Many other participants were suggested and we extended the number of participants as far as we could. With the wide scope of the Symposium program and small format with regard to number, only a few representatives of each major area could be invited. The symposium gave an excellent picture how the various areas are developing. The various methods to treat the many-body problem were thoroughly discussed and many new results were reported. The relativistic many-body
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
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
Macroscopic quantum many-body tunneling of attractive Bose-Einstein condensate in anharmonic trap
NASA Astrophysics Data System (ADS)
Haldar, Sudip Kumar; Debnath, Pankaj Kumar; Chakrabarti, Barnali
2013-09-01
We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter ( λ) is slowly tuned from harmonic to anharmonic. For each choice of λ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with larger number of bosons compared to that in the pure harmonic trap. The transition from resonances to bound states with weak anharmonicity also differs significantly from the earlier study of [N. Moiseyev, L.D. Carr, B.A. Malomed, Y.B. Band, J. Phys. B 37, L193 (2004)]. We also study the tunneling of the metastable condensate very close to the critical number N cr of collapse and observe that near collapse the MQT is the dominant decay mechanism compared to the two-body and three-body loss rate. We also observe the power law behavior in MQT near the critical point. The results for pure harmonic trap are in agreement with mean-field results. However, we fail to retrieve the power law behavior in anharmonic trap although MQT is still the dominant decay mechanism.
Collective many-body van der Waals interactions in molecular systems
DiStasio, Robert A.; von Lilienfeld, O. Anatole; Tkatchenko, Alexandre
2012-01-01
Van der Waals (vdW) interactions are ubiquitous in molecules and condensed matter, and play a crucial role in determining the structure, stability, and function for a wide variety of systems. The accurate prediction of these interactions from first principles is a substantial challenge because they are inherently quantum mechanical phenomena that arise from correlations between many electrons within a given molecular system. We introduce an efficient method that accurately describes the nonadditive many-body vdW energy contributions arising from interactions that cannot be modeled by an effective pairwise approach, and demonstrate that such contributions can significantly exceed the energy of thermal fluctuations—a critical accuracy threshold highly coveted during molecular simulations—in the prediction of several relevant properties. Cases studied include the binding affinity of ellipticine, a DNA-intercalating anticancer agent, the relative energetics between the A- and B-conformations of DNA, and the thermodynamic stability among competing paracetamol molecular crystal polymorphs. Our findings suggest that inclusion of the many-body vdW energy is essential for achieving chemical accuracy and therefore must be accounted for in molecular simulations. PMID:22923693
Many-body Effects in a Laterally Inhomogeneous Semiconductor Quantum Well
NASA Technical Reports Server (NTRS)
Ning, Cun-Zheng; Li, Jian-Zhong; Biegel, Bryan A. (Technical Monitor)
2002-01-01
Many body effects on conduction and diffusion of electrons and holes in a semiconductor quantum well are studied using a microscopic theory. The roles played by the screened Hartree-Fock (SHE) terms and the scattering terms are examined. It is found that the electron and hole conductivities depend only on the scattering terms, while the two-component electron-hole diffusion coefficients depend on both the SHE part and the scattering part. We show that, in the limit of the ambipolax diffusion approximation, however, the diffusion coefficients for carrier density and temperature are independent of electron-hole scattering. In particular, we found that the SHE terms lead to a reduction of density-diffusion coefficients and an increase in temperature-diffusion coefficients. Such a reduction or increase is explained in terms of a density-and temperature dependent energy landscape created by the bandgap renormalization.
Radiative heat transfer in anisotropic many-body systems: Tuning and enhancement
Nikbakht, Moladad
2014-09-07
A general formalism for calculating the radiative heat transfer in many body systems with anisotropic component is presented. Our scheme extends the theory of radiative heat transfer in isotropic many body systems to anisotropic cases. In addition, the radiative heating of the particles by the thermal bath is taken into account in our formula. It is shown that the radiative heat exchange (HE) between anisotropic particles and their radiative cooling/heating (RCH) could be enhanced several order of magnitude than that of isotropic particles. Furthermore, we demonstrate that both the HE and RCH can be tuned dramatically by particles relative orientation in many body systems.
How many-body perturbation theory (MBPT) has changed quantum chemistry
NASA Astrophysics Data System (ADS)
Kutzelnigg, Werner
The history of many-body perturbation theory (MBPT) and its impact on Quantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked-cluster expansion and the time-dependent derivation by Goldstone of such an expansion. A central part of this article is the time-independent formulation of quantum chemistry in Fock space and its diagrammatic representation including the particle-hole picture and the inversion of a commutator. The results of the time-independent derivation of MBPT are compared with those of Goldstone. It is analyzed which ingredients of Goldstone's approach are decisive. The connected diagram theorem is derived both in a constructive way based on a Lie-algebraic formulation and a nonconstructive way making use of the separation theorem. It is discussed why the Goldstone derivation starting from a unitary time-evolution operator, ends up with a wave operator in intermediate normalization. The Møller-Plesset perturbation expansions of Bartlett and Pople are compared. Examples of complete summations of certain classes of diagrams are discussed, for example, that which leads to the Bethe-Goldstone expansion. MBPT for energy differences is analyzed. The paper ends with recent developments and challenges, such as the generalization of normal ordering to arbitrary reference states, contracted Schrödinger k-particle equations and Brillouin conditions, and finally the Nakatsuji theorem and the Nooijen conjecture. Content:text/plain; charset="UTF-8"
NonSymmorphic Symmetry Protected Topological Order in Many-body Localized Systems
NASA Astrophysics Data System (ADS)
Ashraf, Khalid
Many-body localized systems have many interesting physical properties such as localization protected quantum order, symmetry protected topological order, area law in entanglement spectrum etc.. Specifically, it has been shown that closed quantum system in 1D i.e. p-wave superconducting wires host localization protected topological order. In this work, we explore the interplay between non-symmorphic symmetry which protects topological order and localization due to disorder. Using a Bogoliubov-de Gennes (BdG) description of p-wave superconductors, we study the topological edge states on a 2D non-symmorphic crystal. We show that a localization protected topological order can exist at high energy in a 2D non-symmorphic crystal. The system goes between topologically trivial and non-trivial phases based on the degree of disorder and shift between the adjacent atoms in the bipartite lattice. We further explore the nature of this phase transition by calculating the entanglement spectrum of the two phases. Finally, the effect of dimensionality on the realization of these phases are discussed.
Corner transfer matrices for 2D strongly coupled many-body Floquet systems
NASA Astrophysics Data System (ADS)
Kukuljan, Ivan; Prosen, Tomaž
2016-04-01
We develop, based on Baxter’s corner transfer matrices, a renormalizable numerically exact method for computation of the level density of the quasienergy spectra of two-dimensional (2D) locally interacting many-body Floquet systems. We demonstrate its functionality exemplified by the kicked 2D quantum Ising model. Using the method, we are able to treat systems of arbitrarily large finite size (for example lattices of the order of 108 spins). We clearly demonstrate that the density of the Floquet quasienergy spectrum tends to a flat function in the thermodynamic limit for generic values of model parameters. However, contrary to the prediction of random matrices of the circular orthogonal ensemble, the decay rates of the Fourier coefficients of the Floquet level density exhibit rich and non-trivial dependence on the system’s parameters. Remarkably, we find that the method is renormalizable and gives thermodynamically convergent results only in certain regions of the parameter space where the corner transfer matrices have effectively a finite rank for any system size. In the complementary regions, the corner transfer matrices effectively become of full rank and the method becomes non-renormalizable. This may indicate an interesting phase transition from an area- to volume-law of entanglement in the thermodynamic state of a Floquet system.
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.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
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. PMID:20866600
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.
Prethermalization and exponentially slow energy absorption in periodically driven many-body systems
NASA Astrophysics Data System (ADS)
Abanin, Dmitry; Ho, Wen Wei; de Roeck, Wojciech; Huveneers, Francois
We establish some general dynamical properties of lattice many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasi-conserved extensive quantity H*, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well-approximated by the evolution with the Hamiltonian H* up to time τ*, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where H* is ergodic, the driven system prethermalizes to a thermal state described by H* at intermediate times t <τ* , eventually heating up to an infinite-temperature state at times t ~τ* . Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for cold atoms experiments which realize topological states by periodic driving.
PREFACE: Many-body correlations from dilute to dense nuclear systems
NASA Astrophysics Data System (ADS)
Otsuka, Takaharu; Urban, Michael; Yamada, Taiichi
2011-09-01
The International EFES-IN2P3 conference on "Many body correlations from dilute to dense nuclear systems" was held at the Institut Henri Poincaré (IHP), Paris, France, from 15-18 February 2011, on the occasion of the retirement of our colleague Peter Schuck. Correlations play a decisive role in various many-body systems such as nuclear systems, condensed matter and quantum gases. Important examples include: pairing correlations (Cooper pairs) which give rise to nuclear superfluidity (analogous to superconductivity in condensed matter); particle-hole (RPA) correlations in the description of the ground state beyond mean-field theory; clusters; and α-particle correlations in certain nuclei. Also, the nucleons themselves can be viewed as clusters of three quarks. During the past few years, researchers have started to study how the character of these correlations changes with the variation of the density. For instance, the Cooper pairs in dense matter can transform into a Bose-Einstein condensate (BEC) of true bound states at low density (this is the BCS-BEC crossover studied in ultracold Fermi gases). Similar effects play a role in neutron matter at low density, e.g., in the "neutron skin" of exotic nuclei. The α-cluster correlation becomes particularly important at lower density, such as in the excited states of some nuclei (e.g., the α-condensate-like structure in the Hoyle state of 12C) or in the formation of compact stars. In addition to nuclear physics, topics from astrophysics (neutron stars), condensed matter, and quantum gases were discussed in 48 talks and 19 posters, allowing the almost 90 participants from different communities to exchange their ideas, experiences and methods. The conference dinner took place at the Musée d'Orsay, and all the participants enjoyed the very pleasant atmosphere. One session of the conference was dedicated to the celebration of Peter's retirement. We would like to take this opportunity to wish Peter all the best and we hope
Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation
NASA Astrophysics Data System (ADS)
Plimak, L. I.; Weiß, C.; Walser, R.; Schleich, W. P.
2006-08-01
We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a "ferromagnetic" state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.
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.
Morphology of Laplacian growth processes and statistics of equivalent many-body systems
Blumenfeld, R.
1994-11-01
The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes.
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
Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems
NASA Astrophysics Data System (ADS)
Deng, Dong-Ling; Pixley, J. H.; Li, Xiaopeng
We investigate the statistical orthogonality catastrophe (StOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the StOC gives rise to a wave function overlap between the pre- and post-quench ground states that has an exponential decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively ``transported'' to an arbitrary lattice site. We show that in a many-body localized phase, this non-local transport and the associated exponential StOC phenomenon persist in the presence of interactions. We study the possible experimental consequences of the exponential StOC on the Loschmidt echo and spectral function, establishing that this phenomenon might be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy. We thank S.-T. Wang, Z.-X. Gong, Y.-L. Wu, J. D. Sau, and Z. Ovadyahu for discussions. This work is supported by LPS-MPO-CMTC, JQI-NSF-PFC, and ARO-Atomtronics-MURI. The authors acknowledge the University of Maryland supercomputing resources.
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke
We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.
Labud, P A; Ludwig, A; Wieck, A D; Bester, G; Reuter, D
2014-01-31
We present capacitance-voltage spectra for the conduction band states of InAs quantum dots obtained under continuous illumination. The illumination leads to the appearance of additional charging peaks that we attribute to the charging of electrons into quantum dots containing a variable number of illumination-induced holes. By this we demonstrate an electrical measurement of excitonic states in quantum dots. Magnetocapacitance-voltage spectroscopy reveals that the electron always tunnels into the lowest electronic state. This allows us to directly extract, from the highly correlated many-body states, the correlation energy. The results are compared quantitatively to state of the art atomistic configuration interaction calculations, showing very good agreement for a lower level of excitations and also limitations of the approach for an increasing number of particles. Our experiments offer a rare benchmark to many-body theoretical calculations. PMID:24580478
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
The quantified NTO analysis for the electronic excitations of molecular many-body systems
NASA Astrophysics Data System (ADS)
Li, Jian-Hao; Chai, Jeng-Da; Guo, Guang-Yu; Hayashi, Michitoshi
2011-10-01
We show that the origin of electronic transitions of molecular many-body systems can be investigated by a quantified natural transition orbitals (QNTO) analysis and the electronic excitations of the total system can be mapped onto a standard orbitals set of a reference system. We further illustrate QNTO on molecular systems by studying the origin of electronic transitions of DNA moiety, thymine and thymidine. This QNTO analysis also allows us to assess the performance of various functionals used in time-dependent density functional response theory.
New puzzle for many-body systems with random two-body interactions
Johnson, Calvin W.; Nam, Hai Ah
2007-04-15
We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast J=0,2,4,6,8 states. Previous studies, limited only to J=0,2,4 states, had shown strong correlations in boson systems but not fermion systems. By including J{>=}6 states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.
Quantum many-body theory for qubit decoherence in a finite-size spin bath
Yang Wen; Liu Renbao
2008-11-07
We develop a cluster-correlation expansion theory for the many-body dynamics of a finite-size spin bath in a time scale relevant to the decoherence of a center spin or qubit embedded in the bath. By introducing the cluster correlation as the evolution of a group of bath spins divided by the correlations of all the subgroups, the propagator of the whole bath is factorized into the product of all possible cluster correlations. Each cluster-correlation term accounts for the authentic (non-factorizable) collective excitations within that group. Convergent results can be obtained by truncating the cluster-correlation expansion up to a certain cluster size, as verified in an exactly solvable spin-chain model.
Quantum Optical Lattices for Emergent Many-Body Phases of Ultracold Atoms
NASA Astrophysics Data System (ADS)
Caballero-Benitez, Santiago F.; Mekhov, Igor B.
2015-12-01
Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows us to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some phases appear solely due to quantum light-matter correlations. Because of a global, but spatially structured, interaction, the competition between quantum matter and light waves leads to multimode structures even in single-mode cavities, including delocalized dimers of matter-field coherences (bonds), beyond density orders as supersolids and density waves.
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{σ }(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{σ }(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{σ }(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.
Towards quantum many-body physics with Sr in optical lattices
NASA Astrophysics Data System (ADS)
Blatt, Sebastian; Jansa, Nejc; Escudero, Rodrigo G.; Heinz, André; Park, Annie Jihyun; Snigirev, Stepan; Dalibard, Jean; Bloch, Immanuel
2016-05-01
Within the last decade, fermionic alkaline earth atoms in optical lattices have become a platform for precision measurements, culminating in the realization of an atomic clock with the currently highest stability and accuracy at the 2 ×10-18 level. In the meantime, quantum degenerate gases of all bosonic and fermionic isotopes of Sr have been realized. With the extension of the quantum gas microscopy technique to fermionic alkali metal atoms, experiments with quantum degenerate gases in optical lattices have taken another step towards full control over the internal and external degrees of freedom of fermions in optical lattices. Here, we report on the construction of a new experiment with quantum degenerate gases of Sr in optical lattices. Our experiment aims to combine the high spatial control over the atomic degrees of freedom from quantum gas microscopy with the precision control over the internal degrees of freedom enabled by optical lattice clock techniques.
A driven similarity renormalization group approach to quantum many-body problems
Evangelista, Francesco A.
2014-08-07
Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C{sub 2} and F{sub 2}. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.
Numerical computation of dynamically important excited states of many-body systems
NASA Astrophysics Data System (ADS)
Łącki, Mateusz; Delande, Dominique; Zakrzewski, Jakub
2012-07-01
We present an extension of the time-dependent density matrix renormalization group, also known as the time evolving block decimation algorithm, allowing for the computation of dynamically important excited states of one-dimensional many-body systems. We show its practical use for analyzing the dynamical properties and excitations of the Bose-Hubbard model describing ultracold atoms loaded in an optical lattice from a Bose-Einstein condensate. This allows for a deeper understanding of nonadiabaticity in experimental realizations of insulating phases.
Current-carrying quasi-steady states in a periodically driven many-body system
NASA Astrophysics Data System (ADS)
Rudner, Mark; Lindner, Netanel; Berg, Erez
We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially-filled version of Thouless's topologically quantized adiabatic pump. The corresponding single particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For non-integer filling the system is gapless; here the driving cannot be adiabatic and the system is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window where the many-body evolution separately conserves the occupations of the two chiral bands. Within this intermediate time regime we predict that the system reaches a quasi-steady state with uniform crystal momentum occupation within each Floquet band. This state furthermore carries a non-vanishing current given directly by the difference of densities in the right and left moving chiral bands. This remarkable behavior, which holds for both bosons and fermions, may be readily studied experimentally in recently developed cold atom systems.
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.
Code C# for chaos analysis of relativistic many-body systems with reactions
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Stan, E.; Esanu, T.; Felea, D.; Bordeianu, C. C.
2012-04-01
In this work we present a reaction module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross section, particle lifetime, etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincaré section, we propose also the “Clusterization Map”, as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 Collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular π distributions. Catalogue identifier: AEGH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 184 628 No. of bytes in distributed program, including test data, etc.: 7 905 425 Distribution format: tar.gz Programming language: Visual C#.NET 2005 Computer: PC Operating system: Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread. One processor used for each many-body system. RAM: 128 Megabytes Classification: 6.2, 6.5 Catalogue identifier of previous version: AEGH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1464 External routines: Net Framework 2.0 Library Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems with reactions
Lyapunov Modes of Two-Dimensional Many-Body Systems; Soft Disks, Hard Disks, and Rotors
NASA Astrophysics Data System (ADS)
Hoover, Wm. G.; Posch, Harald A.; Forster, Christina; Dellago, Christoph; Zhou, Mary
2002-11-01
The dynamical instability of many-body systems can best be characterized through the local Lyapunov spectrum { λ}, its associated eigenvectors { δ}, and the time-averaged spectrum {< λ>}. Each local Lyapunov exponent λ describes the degree of instability associated with a well-defined direction—given by the associated unit vector δ—in the full many-body phase space. For a variety of hard-particle systems it is by now well-established that several of the δ vectors, all with relatively-small values of the time-averaged exponent < λ>, correspond to quite well-defined long-wavelength "modes." We investigate soft particles from the same viewpoint here, and find no convincing evidence for corresponding modes. The situation is similar—no firm evidence for modes—in a simple two-dimensional lattice-rotor model. We believe that these differences are related to the form of the time-averaged Lyapunov spectrum near < λ>=0.
Entanglement scaling of excited states in large one-dimensional many-body localized systems
NASA Astrophysics Data System (ADS)
Kennes, D. M.; Karrasch, C.
2016-06-01
We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered noninteracting system, where for comparison we compute a quasiexact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of L ˜100 sites and large bond dimensions χ ˜1700 , which allows us to quantitatively analyze the scaling behavior of the entanglement S in the system. The MBL phase is characterized by a logarithmic growth S (L )˜log(L ) over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge.
Distinctive response of many-body localized systems to a strong electric field
NASA Astrophysics Data System (ADS)
Kozarzewski, Maciej; Prelovšek, Peter; Mierzejewski, Marcin
2016-06-01
We study systems that are close to or within the many-body localized (MBL) regime and are driven by a strong electric field. In the ergodic regime, the disorder extends the applicability of the equilibrium linear-response theory to stronger drivings, whereas the response of the MBL systems is very distinctive, revealing currents with damped oscillations. The oscillation frequency is independent of driving and the damping is not due to heating but rather due to dephasing. The details of damping depend on the system's history reflecting the nonergodicity of the MBL phase, while the frequency of the oscillations remains a robust hallmark of localization. Our results suggest that another distinctive characteristic of the driven MBL phase is also a logarithmic increase of the energy and the polarization with time.
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)..
Exploring Few- and Many-Body Dipolar Quantum Phenomena with Ultracold Erbium Atoms
NASA Astrophysics Data System (ADS)
Ferlaino, Francesca
2016-05-01
Given their strong magnetic moment and exotic electronic configuration, rare-earth atoms disclose a plethora of intriguing phenomena in ultracold quantum physics with dipole-dipole interaction. Here, we report on the first degenerate Fermi gas of erbium atoms, based on direct cooling of identical fermions via dipolar collisions. We reveal universal scattering laws between identical dipolar fermions close to zero temperature, and we demonstrate the long-standing prediction of a deformed Fermi surface in dipolar gas. Finally, we present the first experimental study of an extended Bose-Hubbard model using bosonic Er atoms in a three-dimensional optical lattice and we report on the first observation of nearest-neighbor interactions.
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 Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge
NASA Astrophysics Data System (ADS)
Li, Xiaopeng; Ganeshan, Sriram; Pixley, J. H.
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge. JQI-NSF-PFC, AROAtomtronics- MURI, and LPS-CMTC, UMD supercomputing resources.
Many-Body Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge
NASA Astrophysics Data System (ADS)
Li, Xiaopeng; Ganeshan, Sriram; Pixley, J. H.; Das Sarma, S.
2015-10-01
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.
Heating and many-body resonances in a periodically driven two-band system
NASA Astrophysics Data System (ADS)
Bukov, Marin; Heyl, Markus; Huse, David A.; Polkovnikov, Anatoli
2016-04-01
We study the dynamics and stability in a strongly interacting resonantly driven two-band model. Using exact numerical simulations, we find a stable regime at large driving frequencies where the time evolution is governed by a local Floquet Hamiltonian that is approximately conserved out to very long times. For slow driving, on the other hand, the system becomes unstable and heats up to infinite temperature. While thermalization is relatively fast in these two regimes (but to different "temperatures"), in the crossover between them we find slow nonthermalizing time evolution: temporal fluctuations become strong and temporal correlations long lived. Microscopically, we trace back the origin of this nonthermalizing time evolution to the properties of rare Floquet many-body resonances, whose proliferation at lower driving frequency removes the approximate energy conservation, and thus produces thermalization to infinite temperature.
Thermalization and many-body localization in systems under dynamic nuclear polarization
NASA Astrophysics Data System (ADS)
De Luca, Andrea; Rodríguez-Arias, Inés; Müller, Markus; Rosso, Alberto
2016-07-01
We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclear polarization (DNP). We point out that a critical strength of interactions is required to obtain significant nuclear hyperpolarization. Otherwise, the electron spins do not thermalize among each other, due to the incipient many-body localization transition in the electron spin system. Only when the interactions are sufficiently strong, in the so-called spin-temperature regime, they establish an effective thermodynamic behavior in the out-of-equilibrium stationary state. The highest polarization is reached at a point where the spin temperature is just not able to establish itself anymore. We provide numerical predictions for the level of nuclear hyperpolarization and present an analytical technique to estimate the spin temperature as a function of interaction strength and quenched disorder. We show that, at sufficiently strong coupling, nuclear spins perfectly equilibrate to the spin temperature that establishes among the spins of radicals.
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
NASA Astrophysics Data System (ADS)
Bučko, Tomáš; Lebègue, Sébastien; Gould, Tim; Ángyán, János G.
2016-02-01
The energy and gradient expressions for the many-body dispersion scheme (MBD@rsSCS) of Ambrosetti et al (2014 J. Chem. Phys. 140 18A508) needed for an efficient implementation of the method for systems under periodic boundary conditions are reported. The energy is expressed as a sum of contributions from points sampled in the first Brillouin zone, in close analogy with planewave implementations of the RPA method for electrons in the dielectric matrix formulation. By avoiding the handling of large supercells, considerable computational savings can be achieved for materials with small and medium sized unit cells. The new implementation has been tested and used for geometry optimization and energy calculations of inorganic and molecular crystals, and layered materials.
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.
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E; Nooijen, Marcel; Pitzer, Russell; Ramanujam, J; Sadayappan, P
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 multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness. PMID:19888780
Understanding the many-body expansion for large systems. II. Accuracy considerations
NASA Astrophysics Data System (ADS)
Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M.; Herbert, John M.
2016-04-01
To complement our study of the role of finite precision in electronic structure calculations based on a truncated many-body expansion (MBE, or "n-body expansion"), we examine the accuracy of such methods in the present work. Accuracy may be defined either with respect to a supersystem calculation computed at the same level of theory as the n-body calculations, or alternatively with respect to high-quality benchmarks. Both metrics are considered here. In applications to a sequence of water clusters, (H2O)N=6-55 described at the B3LYP/cc-pVDZ level, we obtain mean absolute errors (MAEs) per H2O monomer of ˜1.0 kcal/mol for two-body expansions, where the benchmark is a B3LYP/cc-pVDZ calculation on the entire cluster. Three- and four-body expansions exhibit MAEs of 0.5 and 0.1 kcal/mol/monomer, respectively, without resort to charge embedding. A generalized many-body expansion truncated at two-body terms [GMBE(2)], using 3-4 H2O molecules per fragment, outperforms all of these methods and affords a MAE of ˜0.02 kcal/mol/monomer, also without charge embedding. GMBE(2) requires significantly fewer (although somewhat larger) subsystem calculations as compared to MBE(4), reducing problems associated with floating-point roundoff errors. When compared to high-quality benchmarks, we find that error cancellation often plays a critical role in the success of MBE(n) calculations, even at the four-body level, as basis-set superposition error can compensate for higher-order polarization interactions. A many-body counterpoise correction is introduced for the GMBE, and its two-body truncation [GMBCP(2)] is found to afford good results without error cancellation. Together with a method such as ωB97X-V/aug-cc-pVTZ that can describe both covalent and non-covalent interactions, the GMBE(2)+GMBCP(2) approach provides an accurate, stable, and tractable approach for large systems.
Understanding the many-body expansion for large systems. II. Accuracy considerations.
Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M; Herbert, John M
2016-04-28
To complement our study of the role of finite precision in electronic structure calculations based on a truncated many-body expansion (MBE, or "n-body expansion"), we examine the accuracy of such methods in the present work. Accuracy may be defined either with respect to a supersystem calculation computed at the same level of theory as the n-body calculations, or alternatively with respect to high-quality benchmarks. Both metrics are considered here. In applications to a sequence of water clusters, (H2O)N=6-55 described at the B3LYP/cc-pVDZ level, we obtain mean absolute errors (MAEs) per H2O monomer of ∼1.0 kcal/mol for two-body expansions, where the benchmark is a B3LYP/cc-pVDZ calculation on the entire cluster. Three- and four-body expansions exhibit MAEs of 0.5 and 0.1 kcal/mol/monomer, respectively, without resort to charge embedding. A generalized many-body expansion truncated at two-body terms [GMBE(2)], using 3-4 H2O molecules per fragment, outperforms all of these methods and affords a MAE of ∼0.02 kcal/mol/monomer, also without charge embedding. GMBE(2) requires significantly fewer (although somewhat larger) subsystem calculations as compared to MBE(4), reducing problems associated with floating-point roundoff errors. When compared to high-quality benchmarks, we find that error cancellation often plays a critical role in the success of MBE(n) calculations, even at the four-body level, as basis-set superposition error can compensate for higher-order polarization interactions. A many-body counterpoise correction is introduced for the GMBE, and its two-body truncation [GMBCP(2)] is found to afford good results without error cancellation. Together with a method such as ωB97X-V/aug-cc-pVTZ that can describe both covalent and non-covalent interactions, the GMBE(2)+GMBCP(2) approach provides an accurate, stable, and tractable approach for large systems. PMID:27131529
Many-body 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.
Efficient calculation of many-body induced electrostatics in molecular systems
McLaughlin, Keith Cioce, Christian R.; Pham, Tony; Space, Brian; Belof, Jonathan L.
2013-11-14
Potential energy functions including many-body polarization are in widespread use in simulations of aqueous and biological systems, metal-organics, molecular clusters, and other systems where electronically induced redistribution of charge among local atomic sites is of importance. The polarization interactions, treated here via the methods of Thole and Applequist, while long-ranged, can be computed for moderate-sized periodic systems with extremely high accuracy by extending Ewald summation to the induced fields as demonstrated by Nymand, Sala, and others. These full Ewald polarization calculations, however, are expensive and often limited to very small systems, particularly in Monte Carlo simulations, which may require energy evaluation over several hundred-thousand configurations. For such situations, it shall be shown that sufficiently accurate computation of the polarization energy can be produced in a fraction of the central processing unit (CPU) time by neglecting the long-range extension to the induced fields while applying the long-range treatments of Ewald or Wolf to the static fields; these methods, denoted Ewald E-Static and Wolf E-Static (WES), respectively, provide an effective means to obtain polarization energies for intermediate and large systems including those with several thousand polarizable sites in a fraction of the CPU time. Furthermore, we shall demonstrate a means to optimize the damping for WES calculations via extrapolation from smaller trial systems.
Many-body localization in disorder-free systems: The importance of finite-size constraints
NASA Astrophysics Data System (ADS)
Papić, Z.; Stoudenmire, E. Miles; Abanin, Dmitry A.
2015-11-01
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
NASA Astrophysics Data System (ADS)
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi
Experimental demonstration of Rydberg dressing in a many-body system
NASA Astrophysics Data System (ADS)
Zeiher, Johannes; Schauss, Peter; Hild, Sebastian; Rubio-Abadal, Antonio; Choi, Jae-Yoon; van Bijnen, Rick; Pohl, Thomas; Bloch, Immanuel; Gross, Christian
2016-05-01
Rydberg atoms offer the possibility to study long range interacting systems of ultracold atoms due to their strong van der Waals interactions. Admixture of a Rydberg state to a ground state, known as Rydberg dressing, allows for increased experimental tunability of these interactions and promises to study novel phases of matter. Here we report on our results of the realization of Rydberg dressing in a many-body spin system. Starting from a two-dimensional spin-polarized Mott insulator of an ultracold gas of rubidium-87, we optically couple one spin component to a Rydberg p-state on a single photon ultra-violet transition at 297 nm. Using microwave Ramsey interferometry in the ground state manifold, we measure the spin-spin correlations emerging due to the admixture of long range interactions to the ground state. To show the predicted versatility of Rydberg dressing, we tune the range and anisotropy of the interaction. We furthermore discuss loss processes affecting our dressed ensembles and present initial indications of improved lifetimes in our system. Our results constitute an important step towards the realization of novel spin models with Rydberg dressed interactions.
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions.
Gutiérrez, Ricardo; Garrahan, Juan P; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations-often referred to as the blockade radius-is not a static but rather a dynamic quantity. PMID:26764669
Self-similar nonequilibrium dynamics of a many-body system with power-law interactions
NASA Astrophysics Data System (ADS)
Gutiérrez, Ricardo; Garrahan, Juan P.; Lesanovsky, Igor
2015-12-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-06-01
A simple approach is discussed which associates to (solvable) matrix equations (solvable) dynamical systems, generally interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. We then focus on cases in which the auxiliary variables can be altogether eliminated, reobtaining thereby (via this unified approach) well-known solvable many-body problems, and moreover a (solvable) extension of the "goldfish" model.
NASA Astrophysics Data System (ADS)
Fischer, Uwe R.; Lode, Axel U. Â. J.; Chatterjee, Budhaditya
2015-06-01
The occupation of more than one single-particle state, and hence the emergence of fragmentation, is a many-body phenomenon occurring for systems of spatially confined strongly interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems in single wells. We solve the full many-body Schrödinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method (R-MCTDHB). The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density, and interaction strength is assessed. For contact interactions, it is found that the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long ranged the interactions become. At fixed particle number N , the degree of fragmentation is increasing when the density is decreasing, as expected in one spatial dimension. We demonstrate that this, nontrivially, remains true also for long-range interactions in two spatial dimensions. We, finally, find that fragmentation in a single well is a mesoscopic phenomenon: Within our fully self-consistent approach, the degree of fragmentation, to a good approximation, decreases universally as N-1 /2 when only N is varied.
Sherwin, M.S.; Craig, K.; Unterrainer, K.
1995-12-31
In quantum wells, absorption between the quantized subbands of the conduction band does not take place at the difference of the subband energies; the interactions of the electrons shift the intersubband absorption to higher frequency; this is called the depolarization shift. This shift can be thought of as a dynamic screening effect, and depends upon the difference in population between the subbands of interest. These are the first group of measurements of the dynamics of the depolarization shift, and they offer the possibility of both increased understanding of many-body interactions in real systems, and the possibility of novel quasi-optical devices operating in the far-infared (FIR).
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 (H₂O)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. PMID:25005278
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
Cooperative Shielding in Many-Body Systems with Long-Range Interaction.
Santos, Lea F; Borgonovi, Fausto; Celardo, Giuseppe Luca
2016-06-24
In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with the suppression of propagation. Here, we show that such apparently contradictory behavior is caused by a general property of long-range interacting systems, which we name cooperative shielding. It refers to shielded subspaces that emerge as the system size increases and inside of which the evolution is unaffected by long-range interactions for a long time. As a result, the dynamics strongly depends on the initial state: if it belongs to a shielded subspace, the spreading of perturbation satisfies the Lieb-Robinson bound and may even be suppressed, while for initial states with components in various subspaces, the propagation may be quasi-instantaneous. We establish an analogy between the shielding effect and the onset of quantum Zeno subspaces. The derived effective Zeno Hamiltonian successfully describes the short-ranged dynamics inside the subspaces up to a time scale that increases with system size. Cooperative shielding can be tested in current experiments with trapped ions. PMID:27391705
Cooperative Shielding in Many-Body Systems with Long-Range Interaction
NASA Astrophysics Data System (ADS)
Santos, Lea F.; Borgonovi, Fausto; Celardo, Giuseppe Luca
2016-06-01
In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with the suppression of propagation. Here, we show that such apparently contradictory behavior is caused by a general property of long-range interacting systems, which we name cooperative shielding. It refers to shielded subspaces that emerge as the system size increases and inside of which the evolution is unaffected by long-range interactions for a long time. As a result, the dynamics strongly depends on the initial state: if it belongs to a shielded subspace, the spreading of perturbation satisfies the Lieb-Robinson bound and may even be suppressed, while for initial states with components in various subspaces, the propagation may be quasi-instantaneous. We establish an analogy between the shielding effect and the onset of quantum Zeno subspaces. The derived effective Zeno Hamiltonian successfully describes the short-ranged dynamics inside the subspaces up to a time scale that increases with system size. Cooperative shielding can be tested in current experiments with trapped ions.
Many-body Effects and the Role of Indirect Excitons in Asymmetric InGaAs/GaAs Double Quantum Wells
NASA Astrophysics Data System (ADS)
Smallwood, Christopher; Suzuki, Takeshi; Singh, Rohan; Autry, Travis; Day, Matthew; Jabeen, Fauzia; Cundiff, Steven
In semiconductor research, a fundamental question is how excitons in nearby but distinct spatial locations interact and exchange energy. In quantum well heterostructures, these interactions can be conveniently probed via optical coherent multidimensional spectroscopy (CMDS). Recently, it has been shown using CMDS that reducing the GaAs barrier from 30 nm to 10 nm between two asymmetric InGaAs quantum wells results in interactions driven by many-body effects. Here, we use the technique to show that for narrower barrier thicknesses, the interactions are accompanied by an emergence of spatially indirect excitons. Quantitative measurements of the effects are presented, which will be useful in tailoring GaAs heterostructure devices, and may also inform the role that excitonic interactions play in more complicated systems like microcavity polariton structures and/or photosynthetic light harvesting complexes.
Bold-line Monte Carlo and the nonequilibrium physics of strongly correlated many-body systems
NASA Astrophysics Data System (ADS)
Cohen, Guy
2015-03-01
This talk summarizes real time bold-line diagrammatic Monte-Carlo approaches to quantum impurity models, which make significant headway against the sign problem by summing over corrections to self-consistent diagrammatic expansions rather than a bare diagrammatic series. When the bold-line method is combined with reduced dynamics techniques both local single-time properties and two time correlators such as Green functions can be computed at very long timescales, enabling studies of nonequilibrium steady state behavior of quantum impurity models and creating new solvers for nonequilibrium dynamical mean field theory. This work is supported by NSF DMR 1006282, NSF CHE-1213247, DOE ER 46932, TG-DMR120085 and TG-DMR130036, and the Yad Hanadiv-Rothschild Foundation.
Introduction to the Statistical Physics of Integrable Many-body Systems
NASA Astrophysics Data System (ADS)
Šamaj, Ladislav Å.; Bajnok, Zoltán
2013-05-01
Preface; Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index.
Many-body effects on optical gain in GaAsPN/GaPN quantum well lasers for silicon integration
Park, Seoung-Hwan
2014-02-14
Many-body effects on the optical gain in GaAsPN/GaP QW structures were investigated by using the multiband effective-mass theory and the non-Markovian gain model with many-body effects. The free-carrier model shows that the optical gain peak slightly increases with increasing N composition. In addition, the QW structure with a larger As composition shows a larger optical gain than that with a smaller As composition. On the other hand, in the case of the many-body model, the optical gain peak decreases with increasing N composition. Also, the QW structure with a smaller As composition is observed to have a larger optical gain than that with a larger As composition. This can be explained by the fact that the QW structure with a smaller As or N composition shows a larger Coulomb enhancement effect than that with a larger As or N composition. This means that it is important to consider the many-body effect in obtaining guidelines for device design issues.
Multi-meson systems in lattice QCD / Many-body QCD
Detmold, William
2013-08-31
Nuclear physics entails the study of the properties and interactions of hadrons, such as the proton and neutron, and atomic nuclei and it is central to our understanding of our world at the smallest scales. The underlying basis for nuclear physics is provided by the Standard Model of particle physics which describes how matter interacts through the strong, electromagnetic and weak (electroweak) forces. This theory was developed in the 1970s and provides an extremely successful description of our world at the most fundamental level to which it has been probed. The Standard Model has been, and continues to be, subject to stringent tests at particle accelerators around the world, so far passing without blemish. However, at the relatively low energies that are relevant for nuclear physics, calculations involving the strong interaction, governed by the equations of Quantum Chromodynamics (QCD), are enormously challenging, and to date, the only systematic way to perform them is numerically, using a framework known as lattice QCD (LQCD). In this approach, one discretizes space-time and numerically solves the equations of QCD on a space-time lattice; for realistic calculations, this requires highly optimized algorithms and cutting-edge high performance computing (HPC) resources. Progress over the project period is discussed in detail in the following subsections
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.
NASA Astrophysics Data System (ADS)
Chen, Xuwen; Holmer, Justin
2016-08-01
We consider the dynamics of N bosons in 1D. We assume that the pair interaction is attractive and given by {N^{β-1}V(N^{β}.) where } where {int V ≤slant 0}. We develop new techniques in treating the N-body Hamiltonian so that we overcome the difficulties generated by the attractive interaction and establish new energy estimates. We also prove the optimal 1D collapsing estimate which reduces the regularity requirement in the uniqueness argument by half a derivative. We derive rigorously the 1D focusing cubic NLS with a quadratic trap as the {N → ∞} limit of the N-body dynamic and hence justify the mean-field limit and prove the propagation of chaos for the focusing quantum many-body system.
Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System.
Žnidarič, Marko; Scardicchio, Antonello; Varma, Vipin Kerala
2016-07-22
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects, we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems. PMID:27494464
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.
Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System
NASA Astrophysics Data System (ADS)
Žnidarič, Marko; Scardicchio, Antonello; Varma, Vipin Kerala
2016-07-01
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects, we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.
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.
NASA Astrophysics Data System (ADS)
McKinney, Brett; Watson, Deborah
2000-06-01
We apply low-order dimensional perturbation theory to both the Gross-Pitaevskii equation and to the full many-body Hamiltonian. The perturbation parameter is 1/D, where D is the condensate dimensionality. Unlike the Thomas-Fermi approximation, the zeroth-order DPT solution (Darrow ∞) of the GPE retains a centrifugal term of the kinetic energy. This results in an analytic approximation that is more accurate than TF except for extremely large N where the two approximations agree. The low-order DPT approximation of the full many-body Schrödinger equation for N trapped condensate atoms is an analytic semiclassical approximation that becomes more accurate as the condensate enters a denser regime; precisely the regime where the delta-function potential (pseudopotential) and the GPE should break down. We compare the low-order many-body results for the ground state using the delta-function approximation, which breaks down for high density, with a more realistic interaction potential that reproduces the correct s-wave scattering length.
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.
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.
Description of pairing correlation in many-body finite systems with density functional theory
NASA Astrophysics Data System (ADS)
Hupin, Guillaume; Lacroix, Denis
2011-02-01
Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed earlier [D. Lacroix and G. Hupin, Phys. Rev. BPLRBAQ1098-012110.1103/PhysRevB.82.144509 82, 144509 (2010)] are carefully analyzed. Properties of quasiparticle states projected onto good particle numbers are first reviewed. These properties are used to (i) prove the existence of such a functional, (ii) provide an explicit functional through a 1/N expansion starting from the BCS approach, and (iii) give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picket-fence pairing Hamiltonian where even and odd systems are studied, using the blocking technique, at various particle numbers and coupling strengths, with uniform and random single-particle level spacing. In all cases, very good agreement is found, with a deviation of <1% compared to the exact energy.
Influence of the interaction range on the thermostatistics of a classical many-body system
NASA Astrophysics Data System (ADS)
Cirto, Leonardo J. L.; Assis, Vladimir R. V.; Tsallis, Constantino
2014-01-01
We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/rα (α≥0). The approach is a first principle one (i.e., based on Newton’s law), and yields the probability distribution of momenta. For α large enough and N≫1 we observe, for longstanding states, the Maxwellian distribution, landmark of Boltzmann-Gibbs thermostatistics. But, for α small or comparable to unity, we observe instead robust fat-tailed distributions that are quite well fitted with q-Gaussians. These distributions extremize, under appropriate simple constraints, the nonadditive entropy Sq upon which nonextensive statistical mechanics is based. The whole scenario appears to be consistent with nonergodicity and with the thesis of the q-generalized Central Limit Theorem.
Chord-length and free-path distribution functions for many-body systems
Lu, B. ); Torquato, S. )
1993-04-15
We study fundamental morphological descriptors of disordered media (e.g., heterogeneous materials, liquids, and amorphous solids): [ital the] [ital chord]-[ital length] [ital distribution] [ital function] [ital p]([ital z]) and the [ital free]-[ital path] [ital distribution] [ital function] [ital p]([ital z],[ital a]). For concreteness, we will speak in the language of heterogeneous materials composed of two different materials or phases.'' The probability density function [ital p]([ital z]) describes the distribution of chord lengths in the sample and is of great interest in stereology. For example, the first moment of [ital p]([ital z]) is the mean intercept length'' or mean chord length.'' The chord-length distribution function is of importance in transport phenomena and problems involving discrete free paths'' of point particles (e.g., Knudsen diffusion and radiative transport). The free-path distribution function [ital p]([ital z],[ital a]) takes into account the finite size of a simple particle of radius [ital a] undergoing discrete free-path motion in the heterogeneous material and we show that it is actually the chord-length distribution function for the system in which the pore space'' is the space available to a finite-sized particle of radius [ital a]. Thus it is shown that [ital p]([ital z])=[ital p]([ital z],0). We demonstrate that the functions [ital p]([ital z]) and [ital p]([ital z],[ital a]) are related to another fundamentally important morphological descriptor of disordered media, namely, the so-called lineal-path function [ital L]([ital z]) studied by us in previous work [Phys. Rev. A [bold 45], 922 (1992)]. The lineal path function gives the probability of finding a line segment of length [ital z] wholly in one of the phases'' when randomly thrown into the sample.
Kreula, J M; Clark, S R; Jaksch, D
2016-01-01
We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673
Kreula, J. M.; Clark, S. R.; Jaksch, D.
2016-01-01
We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673
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)
Rihani, J.; Sedrine, N. B.; Sallet, V.; Oueslati, M.; Chtourou, R.
2008-03-01
InAs quantum dots (QDs) on GaAs (0 0 1) substrates were grown by Molecular Beam Epitaxy (MBE) using two growth temperatures. Photoluminescence (PL) pump power dependence measurements at low temperature were carried out for sample grown at higher temperature (520 °C). With increasing excitation density, the ground-state transition energy is found to decrease by 8 meV, while the excited-state transition energies exhibit resonance behaviour. The redshift of the ground-state emission was related to the band-gap renomalization (BGR) effect whereas the blueshift of the excited-state emissions was assigned to the compensation between filling of fine structure states and BGR effects. Using a quasi-resonant PL measurement, we have shown that the renormalization of the band-gap had to occur in the QD barrier.
Diehl, S.; Daley, A. J.; Zoller, P.; Baranov, M.
2010-08-01
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a 'continuous supersolid', which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
NASA Astrophysics Data System (ADS)
Diehl, S.; Baranov, M.; Daley, A. J.; Zoller, P.
2010-08-01
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).10.1103/PhysRevB.82.064509]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a “continuous supersolid,” which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
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
Zheng Huaixiu; Baranger, Harold U.; Gauthier, Daniel J.
2010-12-15
Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light.
Długosz, 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.
Chasman, R.R.
1995-08-01
In the past few years, we developed many-body variational wave functions that allow one to treat pairing and particle-hole two-body interactions on an equal footing. The complexity of these wave functions depends on the number of levels included in the valence space, but does not depend on the number of nucleons in the system. By using residual interaction strengths (e.g. the quadrupole interaction strength or pairing interaction strength) as generator coordinates, one gets many different wave functions, each having a different expectation value for the relevant interaction mode. These wave functions are particularly useful when one is dealing with a situation in which the mean-field approximation is inadequate. Because the same basis states are used in the construction of the many-body wave functions, it is possible to calculate overlaps and interaction matrix elements for the many-body wave functions (which are not in general orthogonal) easily. The valence space can contain a large number of single-particle basis states, when there are constants of motion that can be used to break the levels up into groups. We added a cranking term to the many-body Hamiltonian and modified the projection procedure to get states of good signature before variation. In our present implementation, each group is limited to eight pairs of single-particle levels. We are working on ways of increasing the number of levels that can be included in each group. We are also working on including particle-particle residual interaction modes, in addition to pairing, in our Hamiltonian.
Exploring the many-body localization transition in two dimensions.
Choi, Jae-yoon; Hild, Sebastian; Zeiher, Johannes; Schauß, Peter; Rubio-Abadal, Antonio; Yefsah, Tarik; Khemani, Vedika; Huse, David A; Bloch, Immanuel; Gross, Christian
2016-06-24
A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site-resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers. PMID:27339981
Exploring the many-body localization transition in two dimensions
NASA Astrophysics Data System (ADS)
Choi, Jae-yoon; Hild, Sebastian; Zeiher, Johannes; Schauß, Peter; Rubio-Abadal, Antonio; Yefsah, Tarik; Khemani, Vedika; Huse, David A.; Bloch, Immanuel; Gross, Christian
2016-06-01
A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site–resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.
Many-body localization for disordered Bosons
NASA Astrophysics Data System (ADS)
Stolz, Günter
2016-03-01
Concrete models of interacting quantum systems for which expected manifestations of the many-body localized phase can be rigorously verified are in short supply. Recent work by Seiringer and Warzel (2016 New J. Phys. 18 035002) succeeds in deriving such properties for a disordered Tonks-Girardeau gas. This provides a first example of a Boson gas in the strong Bose glass phase, characterized by the absence of Bose-Einstein condensation as well as the absence of superfluidity at zero temperature. The derivation exploits new mathematical tools to overcome problems arising from the non-locality of Fermionic wave functions associated with the states of a Tonks-Girardeau gas.
NASA Astrophysics Data System (ADS)
Reyes-Lillo, Sebastian E.; Rangel, Tonatiuh; Bruneval, Fabien; Neaton, Jeffrey B.
2016-07-01
The Ruddlesden-Popper (RP) homologous series Srn +1TinO3 n +1 provides a useful template for the study and control of the effects of dimensionality and quantum confinement on the excited state properties of the complex oxide SrTiO3. We use ab initio many-body perturbation theory within the G W approximation and the Bethe-Salpeter equation approach to calculate quasiparticle energies and absorption spectra of Srn +1TinO3 n +1 for n =1 -5 and ∞ . Our computed direct and indirect optical gaps are in excellent agreement with spectroscopic measurements. The calculated optical spectra reproduce the main experimental features and reveal excitonic structure near the gap edge. We find that electron-hole interactions are important across the series, leading to significant exciton binding energies that increase for small n and reach a value of 330 meV for n =1 , a trend attributed to increased quantum confinement. We find that the lowest-energy singlet exciton of Sr2TiO4 (n =1 ) localizes in the two-dimensional plane defined by the TiO2 layer, and we explain the origin of its localization.
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, Ionuţ Mandelshtam, Vladimir A.; Jitomirskaya, Svetlana
2013-11-28
Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCP approximation.
Recent Developments in the Nuclear Many-Body Problem
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.
2002-12-01
The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities and theoretical approaches are opening windows into the richness of many-body phenomena in QCD. A common theme is the use of effective field theory (EFT) methods, which exploit the separation of scales in physical systems. At low energies, effective field theory can explain how existing phenomenology emerges from QCD and how to refine it systematically. More generally, the application of EFT methods to many-body problems promises insight into the analytic structure of observables, the identification of new expansion parameters, and a consistent organisation of many-body corrections, with reliable error estimates.
Kitagawa, Takuya; Pielawa, Susanne; Demler, Eugene; Imambekov, Adilet; Schmiedmayer, Joerg; Gritsev, Vladimir
2010-06-25
We theoretically analyze Ramsey interference experiments in one-dimensional quasicondensates and obtain explicit expressions for the time evolution of full distribution functions of fringe contrast. We show that distribution functions contain unique signatures of the many-body mechanism of decoherence. We argue that Ramsey interference experiments provide a powerful tool for analyzing strongly correlated nature of 1D interacting systems.
Thermalization dynamics in a quenched many-body state
NASA Astrophysics Data System (ADS)
Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus
2016-05-01
Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.
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.
Kim, Won June; Kim, Minho; Lee, Eok Kyun; Lebègue, Sébastien; Kim, Hyungjun
2016-08-18
Previous density functional dispersion corrections to density functional theory lead to an unphysical description of metallic systems, as exemplified by alkali and alkaline earth compounds. We demonstrate that it is possible to remedy this limitation by including screening effects into the form of interacting smeared-out dipoles in the many-body expansion of the interaction. Our new approach, called the coupled fluctuating smeared dipole model, describes equally well noncovalent systems, such as molecular pairs and crystals, and metallic systems. PMID:27487413
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.
NASA Astrophysics Data System (ADS)
Álvarez, Gonzalo A.; Danieli, Ernesto P.; Levstein, Patricia R.; Pastawski, Horacio M.
2007-06-01
An environment interacting with portions of a system leads to multiexponential interaction rates. Within the Keldysh formalism, we fictitiously homogenize the system-environment interaction yielding a uniform decay rate facilitating the evaluation of the propagators. Through an injection procedure we neutralize the fictitious interactions. This technique justifies a stroboscopic representation of the system-environment interaction which is useful for numerical implementation and converges to the natural continuous process. We apply this procedure to a fermionic two-level system and use the Jordan-Wigner transformation to solve a two-spin swapping gate in the presence of a spin environment.
Many-body electron correlations in graphene
NASA Astrophysics Data System (ADS)
Neilson, David; Perali, Andrea; Zarenia, Mohammad
2016-03-01
The conduction electrons in graphene promise new opportunities to access the region of strong many-body electron-electron correlations. Extremely high quality, atomically flat two-dimensional electron sheets and quasi-one-dimensional electron nanoribbons with tuneable band gaps that can be switched on by gates, should exhibit new many-body phenomena that have long been predicted for the regions of phase space where the average Coulomb repulsions between electrons dominate over their Fermi energies. In electron nanoribbons a few nanometres wide etched in monolayers of graphene, the quantum size effects and the van Hove singularities in their density of states further act to enhance electron correlations. For graphene multilayers or nanoribbons in a double unit electron-hole geometry, it is possible for the many-body electron-hole correlations to be made strong enough to stabilise high-temperature electron-hole superfluidity.
Ledvinka, Tomás; Schäfer, Gerhard; Bicák, Jirí
2008-06-27
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. PMID:18643648
Strong Disorder Renormalization Group for the Many Body Localization Transition
NASA Astrophysics Data System (ADS)
Refael, Gil; Oganesyan, Vadim; Iyer, Shankar
2012-02-01
The strong disorder renormalization group, originally devised by Ma and Dasgupta to study the random Heisenberg antiferromagnet, has subsequently been used to investigate the low energy physics and quantum phase transitions of a variety of strongly disordered systems. However, recent work by Basko, Aleiner, and Altshuler has focused attention on the many body localization transition, a dynamical quantum phase transition that involves the localization of highly excited eigenstates of a many body system in Fock space. Numerical results from an exact diagonalization study by Pal and Huse suggest that the many body localization transition may exhibit so-called infinite-randomness, a property that implies that a strong disorder renormalization group may be well-suited to study this transition. With the many body localization transition in mind, we therefore outline a strong disorder renormalization procedure that targets the least-localized eigenstate of a model. We then apply this procedure to study disordered quantum Ising and XXZ models. The latter model is similar to the one investigated by Pal and Huse and is expected to contain a dynamical transition between localized and ergodic phases; our principal aim is to use the strong disorder RG to characterize this transition.
Many body topics in condensed matter physics
NASA Astrophysics Data System (ADS)
Anduaga, Inaki Pablo
Two different problems involving many-body systems are presented. A hydrodynamic version of the Calogero system of one-dimensional particles interacting on the line is derived using a classical field formalism, and the results are contrasted to a derivation starting from first quantum mechanical principles. This new classical approach is shown to help in understanding subtleties occurring in the latter, such as the conditions for chiral motion, the decomposition of the Hamiltonian in terms of chiral currents and the nature of the physical velocity and density operators. Explicit collective solitonic excitations in the linear and non-linear limits are also presented. Additionally, we overview the possibility of expanding this formalism to the study of the Fractional Quantum Hall Effect. The second problem involves a simple two-dimensional model of a px + ipy superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubovde Gennes operator. The results confirm theoretical predictions such as the Thomas-Fermi approximation and the Ishikawa formula, in which the mass flow at zero-temperature and for a constant director l follows jmass = ½curl(rhohl/2).
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2016-07-01
The iterative methods to diagonalize matrices and many-body Hamiltonians can be reformulated as flows of Hamiltonians towards diagonalization driven by unitary transformations that preserve the spectrum. After a comparative overview of the various types of discrete flows (Jacobi, QR-algorithm) and differential flows (Toda, Wegner, White) that have been introduced in the past, we focus on the random XXZ chain with random fields in order to determine the best closed flow within a given subspace of running Hamiltonians. For the special case of the free-fermion random XX chain with random fields, the flow coincides with the Toda differential flow for tridiagonal matrices which is related to the classical integrable Toda chain and which can be seen as the continuous analog of the discrete QR-algorithm. For the random XXZ chain with random fields that displays a many-body-localization transition, the present differential flow should be an interesting alternative to compare with the discrete flow that has been proposed recently to study the many-body-localization properties in a model of interacting fermions (Rademaker and Ortuno 2016 Phys. Rev. Lett. 116, 010404).
NASA Astrophysics Data System (ADS)
Boyle, J. J.; Pindzola, M. S.
2005-11-01
Preface; Contributors; Introduction; Part I. Atomic Structure: 1. Development of atomic many-body theory Ingvar Lindgren; 2. Relativistic MBPT for highly charged ions W. R. Johnson; 3. Parity nonconservation in atoms S. A. Blundell, W. R. Johnson, and J. Sapirstein; Part II. Photoionization of Atoms: 4. Single photoionization processes J. J. Boyle, and M. D. Kutzner; 5. Photoionization dominated by double excitation T. N. Chang; 6. Direct double photoionization in atoms Z. W. Liu; 7. Photoelectron angular distributions Steven T. Manson; Part III. A. Atomic Scattering - General Considerations: 8. The many-body approach to electron-atom collisions M. Ya Amusia; 9. Theoretical aspects of electron impact ionization P. L. Altick; Part III. B. Atomic Scattering - Low-Order Applications: 10. Perturbation series methods D. H. Madison; 11. Target dependence of the triply differential cross section Cheng Pan and Anthony F. Starace; 12. Overview of Thomas processes for fast mass transfer J. H. McGuire, Jack C. Straton and T. Ishihara; Part III. C. Atomic Scattering - All-Order Applications: 13. R-matrix Theory: Some Recent Applications Philip G. Burke: 14. Electron scattering: application of Dirac R-matrix theory Wasantha Wijesundera, Ian Grant and Patrick Norrington; 15. Close coupling and distorted-wave theory D. C. Griffin and M. S. Pindzola; Appendix: Units and notation; References; Index.
NASA Astrophysics Data System (ADS)
Boyle, J. J.; Pindzola, M. S.
1998-09-01
Preface; Contributors; Introduction; Part I. Atomic Structure: 1. Development of atomic many-body theory Ingvar Lindgren; 2. Relativistic MBPT for highly charged ions W. R. Johnson; 3. Parity nonconservation in atoms S. A. Blundell, W. R. Johnson, and J. Sapirstein; Part II. Photoionization of Atoms: 4. Single photoionization processes J. J. Boyle, and M. D. Kutzner; 5. Photoionization dominated by double excitation T. N. Chang; 6. Direct double photoionization in atoms Z. W. Liu; 7. Photoelectron angular distributions Steven T. Manson; Part III. A. Atomic Scattering - General Considerations: 8. The many-body approach to electron-atom collisions M. Ya Amusia; 9. Theoretical aspects of electron impact ionization P. L. Altick; Part III. B. Atomic Scattering - Low-Order Applications: 10. Perturbation series methods D. H. Madison; 11. Target dependence of the triply differential cross section Cheng Pan and Anthony F. Starace; 12. Overview of Thomas processes for fast mass transfer J. H. McGuire, Jack C. Straton and T. Ishihara; Part III. C. Atomic Scattering - All-Order Applications: 13. R-matrix Theory: Some Recent Applications Philip G. Burke: 14. Electron scattering: application of Dirac R-matrix theory Wasantha Wijesundera, Ian Grant and Patrick Norrington; 15. Close coupling and distorted-wave theory D. C. Griffin and M. S. Pindzola; Appendix: Units and notation; References; Index.
Probing many-body interactions in an optical lattice clock
Rey, A.M.; Gorshkov, A.V.; Kraus, C.V.; Martin, M.J.; 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.
Interferometric measurement of many-body topological invariants using polarons
NASA Astrophysics Data System (ADS)
Grusdt, Fabian; Yao, Norman; Abanin, Dmitry; Demler, Eugene
2014-05-01
We present a scheme for the direct detection of many-body topological invariants in ultra cold quantum gases in optical lattices. We generalize single-particle interferometric schemes developed for the detection of topologically non-trivial band structures [Atala et al., Nature Physics 9, 795 (2013)] by coupling a spin-1/2 impurity to a (topological) excitation of an interacting many-body system. Performing Ramsey interferometry in combination with Bloch oscillations of the resulting polaronic particle allows to directly detect the many body-topological invariant. In particular we consider adiabatic Thouless pumps in the super-lattice Bose-Hubbard model, which transport a quantized amount of particles across a one-dimensional lattice. In the presence of inter-atomic interactions this quantized current is given by a many-body Chern number, which can be measured using our protocol. These systems also support symmetry-protected topological phases, the invariants of which can be obtained from our protocol as well.
Coccia, Emanuele; Varsano, Daniele; Guidoni, Leonardo
2016-01-01
In this letter, we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) Å, larger than the values obtained by DFT (PBE, B3LYP, and CAM-B3LYP) and shorter than that calculated at the Hartree–Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO–LUMO major contribution of the Bu+-like (S2) bright excited state. Many Body Green’s Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu+-like state for the VMC structure (VMC/MBGFT) provide an excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed. PMID:26580027
Many-body localization: Entanglement and efficient numerical simulations
NASA Astrophysics Data System (ADS)
Pollmann, Frank
Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new efficient numerical methods to find highly excited many-body eigenstates is essential. In this talk, we will discuss two complimentary approaches to simulate MBL systems: First, we introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate to large disorder. This method explicitly takes advantage of the local spatial structure and the low entanglement which is characteristic for MBL eigenstates. Second, we propose an approach to directly find an approximate compact representation of the diagonalizing unitary by using a variational unitary matrix-product operator.
Observing a self-thermalizing many-body state
NASA Astrophysics Data System (ADS)
Lukin, Alexander; Tai, Eric; Preiss, Philipp; Rispoli, Matthew; Robert, Schittko; Kaufman, Adam; Greiner, Markus
2016-05-01
There is a clear intuition for the dynamics of a classical many-body system that is suddenly displaced from thermal equilibrium: Unless there are conserved quantities, the system re-thermalizes and reaches a new equilibrium distribution constrained by only a few thermodynamic variables. In contrast, an isolated quantum many-body system subject to a sudden perturbation undergoes unitary evolution. The dynamics is reversible and preserves memory of the microscopic details of the initial state. Yet, the long-time behavior of local observables in quenched, non-integrable systems is very well described by thermal ensembles. This thermalization within globally pure quantum states is mediated by the growth of entanglement entropy, which takes on the role of thermodynamic entropy. We use recently developed methods to study the global and local quantum purity in the dynamics of quenched Bose-Hubbard systems. We observe a rapid growth and saturation of the entanglement entropy, during which the full system remains verifiably pure. Using number-resolved measurements in a quantum gas microscope, we show that local observables thermalize in agreement with the Eigenstate Thermalization Hypothesis, and we detect a near-volume law in the entanglement entropy.
Interferometric measurements of many-body topological invariants using mobile impurities
NASA Astrophysics Data System (ADS)
Grusdt, F.; Yao, N. Y.; Abanin, D.; Fleischhauer, M.; Demler, E.
2016-06-01
Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable.
Sliusarenko, O. Yu.; Chechkin, A. V.; Slyusarenko, Yu. V.
2015-04-15
By generalizing Bogolyubov’s reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton’s equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the single-particle distribution function, we use a regular cutoff procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation, we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases are discussed by assuming either Gaussian statistics of external perturbation or homogeneity of the system.
Parametric excitation and squeezing in a many-body spinor condensate
NASA Astrophysics Data System (ADS)
Hoang, T. M.; Anquez, M.; Robbins, B. A.; Yang, X. Y.; Land, B. J.; Hamley, C. D.; Chapman, M. S.
2016-04-01
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states.
Parametric excitation and squeezing in a many-body spinor condensate.
Hoang, T M; Anquez, M; Robbins, B A; Yang, X Y; Land, B J; Hamley, C D; Chapman, M S
2016-01-01
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states. PMID:27044675
Parametric excitation and squeezing in a many-body spinor condensate
Hoang, T. M.; Anquez, M.; Robbins, B. A.; Yang, X. Y.; Land, B. J.; Hamley, C. D.; Chapman, M. S.
2016-01-01
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states. PMID:27044675
Universal dynamics across many-body localization phase transition
NASA Astrophysics Data System (ADS)
Serbyn, Maksym
Many body localization allows quantum systems to evade thermalization owing to the emergence of extensive number of local conserved quantities. Many-body localized (MBL) systems exhibit universal dynamics, qualitatively distinct from dynamics in ergodic systems. In this talk I will survey recent progress in understanding the properties of the MBL phase, which follow from the picture of local conserved quantities. In particular, I will discuss the power-law relaxation of local observables, which gives an experimentally observable signatures of the MBL phase. In the second part of my talk, I will demonstrate how the delocalization transition can be probed by characterizing the breakdown of local conservation laws. Using statistics of matrix elements of local operators, I will introduce an analogue of many-body Thouless conductance which probes the response of the system to local perturbations. Its scaling allows one to locate the MBL transition, and predicts the onset of logarithmically slow transport at the MBL transition, consistent with results from the renormalization group. In addition, I will demonstrate how the properties of matrix elements govern the crossover of the level statistics across the MBL transition, and relate to the dynamics in the ergodic phase. I will conclude by discussing experimental implications and open challenges in understanding the MBL transition.
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.
Many-body entanglement in decoherence processes
McAneney, Helen; Lee, Jinhyoung; Kim, M.S.
2003-12-01
A pure state decoheres into a mixed state as it entangles with an environment. When an entangled two-mode system is embedded in a thermal environment, however, each mode may not be entangled with its environment by their simple linear interaction. We consider an exactly solvable model to study the dynamics of a total system, which is composed of an entangled two-mode system and a thermal environment. The Markovian interaction with the environment is concerned with an array of infinite number of beam splitters. It is shown that many-body entanglement of the system and the environment may play a crucial role in the process of disentangling the system.
NASA Astrophysics Data System (ADS)
Umezawa, Naoto; Austin, Brian; Lester, William A., Jr.
2009-03-01
An efficient method of optimizing a Slater determinant, D, in the Jastrow-Slater-type wave function, FD, is suggested. Here, the so-called transcorrelated Hamiltonian, 1F H F, which is a similarity transformation of the usual Hamiltonian of an electronic system with respect to a Jastrow function F, is fitted to an effective Hamiltonian, Heff= ∑i^N ( -12 2̂i+ v(ri) ), in which all the electron-electron and electron-neucleus interactions are represented by a one-body potential, v(r). A single-particle Schr"odinger equation is then solved by using v(r) to determine the orbitals, of which the Slater determinant consists. The obtained orbitals improve the atomic total energies in the variational Monte Carlo calculations compared to those given by the density-functional-based orbitals. Advantages of using the optimized orbitals in the diffusion Monte Carlo calculations are also discussed.
Many-body radiative heat transfer theory.
Ben-Abdallah, Philippe; Biehs, Svend-Age; Joulain, Karl
2011-09-01
In this Letter, an N-body theory for the radiative heat exchange in thermally nonequilibrated discrete systems of finite size objects is presented. We report strong exaltation effects of heat flux which can be explained only by taking into account the presence of many-body interactions. Our theory extends the standard Polder and van Hove stochastic formalism used to evaluate heat exchanges between two objects isolated from their environment to a collection of objects in mutual interaction. It gives a natural theoretical framework to investigate the photon heat transport properties of complex systems at the mesoscopic scale. PMID:22026672
Studying non-equilibrium many-body dynamics using one-dimensional Bose gases
Langen, Tim; Gring, Michael; Kuhnert, Maximilian; Rauer, Bernhard; Geiger, Remi; Mazets, Igor; Smith, David Adu; Schmiedmayer, Jörg; Kitagawa, Takuya; Demler, Eugene
2014-12-04
Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.
Stochastic gene expression as a many-body problem
Sasai, Masaki; Wolynes, Peter G.
2003-01-01
Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks. PMID:12606710
Many-Body Models for Molecular Nanomagnets
NASA Astrophysics Data System (ADS)
Chiesa, A.; Carretta, S.; Santini, P.; Amoretti, G.; Pavarini, E.
2013-04-01
We present a flexible and effective ab initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as a one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni, and the single-molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.
Koch, D; Fertitta, E; Paulus, B
2016-07-14
Due to the importance of both static and dynamical correlation in the bond formation, low-dimensional beryllium systems constitute interesting case studies to test correlation methods. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. To gain insight into the main characteristics of the wave function, we started by focusing on the description of small Be chains using standard quantum chemical methods. In a next step we applied the MoI to larger beryllium systems, starting from the Be6 ring. The complete active space formalism was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Although this is a well-established approach for systems with limited multireference character, its application regarding the description of whole dissociation curves requires further testing. Subsequent to the discussion of the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain. PMID:27421394
NASA Astrophysics Data System (ADS)
Koch, D.; Fertitta, E.; Paulus, B.
2016-07-01
Due to the importance of both static and dynamical correlation in the bond formation, low-dimensional beryllium systems constitute interesting case studies to test correlation methods. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. To gain insight into the main characteristics of the wave function, we started by focusing on the description of small Be chains using standard quantum chemical methods. In a next step we applied the MoI to larger beryllium systems, starting from the Be6 ring. The complete active space formalism was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Although this is a well-established approach for systems with limited multireference character, its application regarding the description of whole dissociation curves requires further testing. Subsequent to the discussion of the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain.
NASA Astrophysics Data System (ADS)
Réal, Florent; Vallet, Valérie; Flament, Jean-Pierre; Masella, Michel
2013-09-01
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.
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
Relativistically Covariant Many-Body Perturbation Procedure
NASA Astrophysics Data System (ADS)
Lindgren, Ingvar; Salomonson, Sten; Hedendahl, Daniel
A covariant evolution operator (CEO) can be constructed, representing the time evolution of the relativistic wave unction or state vector. Like the nonrelativistic version, it contains (quasi-)singularities. The regular part is referred to as the Green’s operator (GO), which is the operator analogue of the Green’s function (GF). This operator, which is a field-theoretical concept, is closely related to the many-body wave operator and effective Hamiltonian, and it is the basic tool for our unified theory. The GO leads, when the perturbation is carried to all orders, to the Bethe-Salpeter equation (BSE) in the equal-time or effective-potential approximation. When relaxing the equal-time restriction, the procedure is fully compatible with the exact BSE. The calculations are performed in the photonic Fock space, where the number of photons is no longer constant. The procedure has been applied to helium-like ions, and the results agree well with S-matrix results in cases when comparison can be performed. In addition, evaluation of higher-order quantum-electrodynamical (QED) correlational effects has been performed, and the effects are found to be quite significant for light and medium-heavy ions.
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.
Factorization in large-scale many-body calculations
Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.
2013-08-07
One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elementsmore » on the fly and can reduce the storage requirements by an order of magnitude or more. Here, we discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.« less
Factorization in large-scale many-body calculations
Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.
2013-08-07
One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elements on the fly and can reduce the storage requirements by an order of magnitude or more. Here, we discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.
Factorization in large-scale many-body calculations
NASA Astrophysics Data System (ADS)
Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.
2013-12-01
One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elements on the fly and can reduce the storage requirements by an order of magnitude or more. We discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.
NASA Astrophysics Data System (ADS)
Molavian, Hamid R.; Gingras, Michel J. P.; Canals, Benjamin
2007-04-01
The Tb2Ti2O7 pyrochlore magnetic material is attracting much attention for its spin liquid state, failing to develop long-range order down to 50 mK despite a Curie-Weiss temperature θCW˜-14K. In this Letter we reinvestigate the theoretical description of this material by considering a quantum model of independent tetrahedra to describe its low-temperature properties. The naturally tuned proximity of this system near a Néel to spin ice phase boundary allows for a resurgence of quantum fluctuation effects that lead to an important renormalization of its effective low-energy spin Hamiltonian. As a result, Tb2Ti2O7 is argued to be a quantum spin ice. We put forward an experimental test of this proposal using neutron scattering on a single crystal.
Many-body localization as percolation in d >1
NASA Astrophysics Data System (ADS)
Chandran, Anushya; Laumann, Chris; Gottesman, Daniel
2015-03-01
Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration. Isolated quantum systems need not equilibrate; this is the phenomenon of many-body localization (MBL). While a detailed understanding of MBL and the associated delocalization transition is beginning to emerge in one dimension, relatively little is known about higher dimensions. In this work, we present a minimal tractable model for MBL in all spatial dimensions. Specifically, we analyze a disordered Floquet circuit composed of Clifford gates. In one dimension, the system is always localized, while in higher dimensions, it exhibits both delocalized and localized phases. The localized phase consists of well-defined metallic puddles embedded in an insulating matrix. When the puddles percolate, the system delocalizes; this maps the dynamical transition to critical percolation. We also comment on the stability of the phases to generic perturbations away from the Clifford class.
Spectral statistics across the many-body localization transition
NASA Astrophysics Data System (ADS)
Serbyn, Maksym; Moore, Joel E.
2016-01-01
The many-body localization transition (MBLT) between ergodic and many-body localized phases in disordered interacting systems is a subject of much recent interest. The statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, a fractal enhancement of matrix elements upon approaching the MBLT from the delocalized side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interactions and the level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories.
Many body population trapping in ultracold dipolar gases
NASA Astrophysics Data System (ADS)
Dutta, Omjyoti; Lewenstein, Maciej; Zakrzewski, Jakub
2014-05-01
A system of interacting dipoles is of paramount importance for understanding many-body physics. The interaction between dipoles is anisotropic and long-range. While the former allows one to observe rich effects due to different geometries of the system, long-range (1/{{r}^{3}}) interactions lead to strong correlations between dipoles and frustration. In effect, interacting dipoles in a lattice form a paradigmatic system with strong correlations and exotic properties with possible applications in quantum information technologies, and as quantum simulators of condensed matter physics, material science, etc. Notably, such a system is extremely difficult to model due to a proliferation of interaction induced multi-band excitations for sufficiently strong dipole-dipole interactions. In this article we develop a consistent theoretical model of interacting polar molecules in a lattice by applying the concepts and ideas of ionization theory which allows us to include highly excited Bloch bands. Additionally, by involving concepts from quantum optics (population trapping), we show that one can induce frustration and engineer exotic states, such as Majumdar-Ghosh state, or vector-chiral states in such a system.
Dynamical stability of a many-body Kapitza pendulum
Citro, Roberta; Dalla Torre, Emanuele G.; D’Alessio, Luca; Polkovnikov, Anatoli; Babadi, Mehrtash; Oka, Takashi; Demler, Eugene
2015-09-15
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.
The semiclassical propagator in Fock space: dynamical echo and many-body interference.
Engl, Thomas; Urbina, Juan Diego; Richter, Klaus
2016-06-13
We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particle contributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal. PMID:27140976
Many-Body Dispersion Interactions in Molecular Materials
NASA Astrophysics Data System (ADS)
Distasio, Robert A., Jr.
2015-03-01
In this work, we have developed an efficient method for obtaining an accurate theoretical description of van der Waals (vdW) interactions that includes both long-range Coulomb electrodynamic response screening effects as well as treatment of the many-body vdW energy to infinite order. This method goes beyond the standard C6 /R6 pairwise additive approximation and can easily be coupled to a wide array of theoretical methods, ranging from classical force fields to higher-level quantum chemical calculations. To demonstrate the increasingly important role played by many-body vdW interactions in large, structurally complex molecular systems, we use this method to investigate several pertinent molecular properties, such as binding energies/affinities in gas-phase molecular dimers and supramolecular complexes, relative conformational energetics in small polypeptides, and thermodynamic stabilities among competing molecular crystal polymorphs. This work received funding from the Department of Energy under Grant Nos.: DOE DE-SC0008626 and DOE DE-FG02ER46201 and the European Research Council (ERC Starting Grant VDW-CMAT).
Aiming for benchmark accuracy with the many-body expansion.
Richard, Ryan M; Lao, Ka Un; Herbert, John M
2014-09-16
Conspectus The past 15 years have witnessed an explosion of activity in the field of fragment-based quantum chemistry, whereby ab initio electronic structure calculations are performed on very large systems by decomposing them into a large number of relatively small subsystem calculations and then reassembling the subsystem data in order to approximate supersystem properties. Most of these methods are based, at some level, on the so-called many-body (or "n-body") expansion, which ultimately requires calculations on monomers, dimers, ..., n-mers of fragments. To the extent that a low-order n-body expansion can reproduce supersystem properties, such methods replace an intractable supersystem calculation with a large number of easily distributable subsystem calculations. This holds great promise for performing, for example, "gold standard" CCSD(T) calculations on large molecules, clusters, and condensed-phase systems. The literature is awash in a litany of fragment-based methods, each with their own working equations and terminology, which presents a formidable language barrier to the uninitiated reader. We have sought to unify these methods under a common formalism, by means of a generalized many-body expansion that provides a universal energy formula encompassing not only traditional n-body cluster expansions but also methods designed for macromolecules, in which the supersystem is decomposed into overlapping fragments. This formalism allows various fragment-based methods to be systematically classified, primarily according to how the fragments are constructed and how higher-order n-body interactions are approximated. This classification furthermore suggests systematic ways to improve the accuracy. Whereas n-body approaches have been thoroughly tested at low levels of theory in small noncovalent clusters, we have begun to explore the efficacy of these methods for large systems, with the goal of reproducing benchmark-quality calculations, ideally meaning complete
Nonequilibrium dissipation-driven steady many-body entanglement
NASA Astrophysics Data System (ADS)
Bellomo, Bruno; Antezza, Mauro
2015-04-01
We study an ensemble of two-level quantum systems (qubits) interacting with a common electromagnetic field in the proximity of a dielectric slab whose temperature is held different from that of some far surrounding walls. We show that the dissipative dynamics of the qubits driven by this stationary and out of thermal equilibrium field allows the production of steady many-body entangled states, different from the case at thermal equilibrium where steady states are always nonentangled. By studying up to ten qubits, we point out the role of symmetry in the entanglement production, which is exalted in the case of permutationally invariant configurations. In the case of three qubits, we find a strong dependence of tripartite entanglement on the spatial disposition of the qubits, and in the case of six qubits we find several highly entangled bipartitions where entanglement can, remarkably, survive for large qubit-qubit distances up to 100 μ m .
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.
Many-Body Interactions and Nuclear Structure
Hjorth-Jensen, M.; Dean, David Jarvis; Hagen, Gaute; Kvaal, S.
2010-01-01
This article presents several challenges to nuclear many-body theory and our understanding of the stability of nuclear matter. In order to achieve this, we present five different cases, starting with an idealized toy model. These cases expose problems that need to be understood in order to match recent advances in nuclear theory with current experimental programs in low-energy nuclear physics. In particular, we focus on our current understanding, or lack thereof, of many-body forces, and how they evolve as functions of the number of particles. We provide examples of discrepancies between theory and experiment and outline some selected perspectives for future research directions.
High precision framework for chaos many-body engine
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Felea, D.; Jipa, Al.
2014-04-01
In this paper we present a C# 4.0 high precision framework for simulation of relativistic many-body systems. In order to benefit from the, previously developed, chaos analysis instruments, all new modules were integrated with Chaos Many-Body Engine (Grossu et al. 2010, 2013). As a direct application, we used 46 digits precision for analyzing the "Butterfly Effect" of the gravitational force in a specific relativistic nuclear collision toy-model.
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.
Towards Efficient and General Method for Many-Body van-der-Waals Interactions
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2012-02-01
Van der Waals interactions are intrinsically many-body phenomena, arising from collective electron fluctuations in a given material. Adiabatic connection fluctuation-dissipation theorem (ACFDT) allows to compute the many-body vdW interactions accurately. However, the ACFDT computational cost is prohibitive for real materials, even when the random-phase approximation is employed for the response function. We show how the problem of computing the long-range many-body vdW energy for real systems can be solved efficiently by mapping the system (molecule or condensed matter) onto a collection of quantum harmonic oscillators. Currently, our method, which couples density-functional theory with the many-body dispersion energy (DFT+MBD), is developed for non-metallic system [A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, submitted]. The DFT+MBD method includes the hybridization effects by using the Tkatchenko-Scheffler approach [PRL 102, 073005 (2009)], the long-range Coulomb screening through classical electrodynamics [B. U. Felderhof, Physica 29, 1569 (1974)], and the many-body vdW energy from the coupled-fluctuating dipole model [M. W. Cole et al., Mol. Simul. 35, 849 (2009)]. The successes of the DFT+MBD approach and the many challenges that lie ahead will be discussed.
Interferometric measurements of many-body topological invariants using mobile impurities
Grusdt, F.; Yao, N. Y.; Abanin, D.; Fleischhauer, M.; Demler, E.
2016-01-01
Topological quantum phases cannot be characterized by Ginzburg–Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable. PMID:27312285
Interferometric measurements of many-body topological invariants using mobile impurities.
Grusdt, F; Yao, N Y; Abanin, D; Fleischhauer, M; Demler, E
2016-01-01
Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable. PMID:27312285
Projection techniques to approach the nuclear many-body problem
NASA Astrophysics Data System (ADS)
Sun, Yang
2016-04-01
Our understanding of angular-momentum-projection goes beyond quantum-number restoration for symmetry-violated states. The angular-momentum-projection method can be viewed as an efficient way of truncating the shell-model space which is otherwise too large to handle. It defines a transformation from the intrinsic system, where dominant excitation modes in the low-energy region are identified with the concept of spontaneous symmetry breaking, to the laboratory frame with well-organized configuration states according to excitations. An energy-dictated, physically-guided shell-model truncation can then be carried out within the projected space and the Hamiltonian is thereby diagonalized in a compact basis. The present article reviews the theory of angular-momentum-projection applied in the nuclear many-body problem. Angular momentum projection emerges naturally if a deformed state is treated quantum-mechanically. To demonstrate how different physical problems in heavy, deformed nuclei can be efficiently described with different truncation schemes, we introduce the projected shell model and show examples of calculation in a basis with axial symmetry, a basis with triaxiality, and a basis with both quasiparticle and phonon excitations. Technical details of how to calculate the projected matrix elements and how to build a workable model with the projection techniques are given in the appendix.
Absence of many-body mobility edges
NASA Astrophysics Data System (ADS)
De Roeck, Wojciech; Huveneers, Francois; Müller, Markus; Schiulaz, Mauro
2016-01-01
Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur is lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.
PREFACE: 17th International Conference on Recent Progress in Many-Body Theories (MBT17)
NASA Astrophysics Data System (ADS)
Reinholz, Heidi; Boronat, Jordi
2014-08-01
These are the proceedings of the XVII International Conference on Recent Progress in Many-Body Theories, which was held from 8-13 September 2013 in Rostock, Germany. The conference continued the triennial series initiated in Trieste in 1978 and was devoted to new developments in the field of many-body theories. The conference series encourages the exchange of ideas between physicists working in such diverse areas as nuclear physics, quantum chemistry, lattice Hamiltonians or quantum uids. Many-body theories are an integral part in different fields of theoretical physics such as condensed matter, nuclear matter and field theory. Phase transitions and macroscopic quantum effects such as magnetism, Bose-Einstein condensation, super uidity or superconductivity have been investigated within ultra-cold gases, finite systems or various nanomaterials. The conference series on Recent Progress in Many-Body Theories is devoted to foster the interaction and to cross-fertilize between different fields and to discuss future lines of research. The topics of the 17th meeting were Cluster Physics Cold Gases High Energy Density Matter and Intense Lasers Magnetism New Developments in Many-Body Techniques Nuclear Many-Body and Relativistic Theories Quantum Fluids and Solids Quantum Phase Transitions Topological Insulators and Low Dimensional Systems. 109 participants from 20 countries participated. 44 talks and 61 posters werde presented. As a particular highlight of the conference, The Eugene Feenberg Memorial Medal for outstanding results in the field of many-body theory and The Hermann Kümmel Early Achievement Award in Many-Body Physics for young scientists in that field were awarded. The Feenberg Medal went jointly to Patrick Lee (MIT, USA) for his fundamental contributions to condensed-matter theory, especially in regard to the quantum Hall effect, to universal conductance uctuations, and to the Kondo effect in quantum dots, and Douglas Scalapino (UC Santa Barbara, USA) for his
Geometric stability of the many-body localized phase in two and higher dimensions
NASA Astrophysics Data System (ADS)
Chandran, Anushya; Pal, Arijeet; Laumann, Chris; Scardicchio, Antonello
Isolated disordered quantum systems need not equilibrate and be described by statistical mechanics; this is the phenomenon of many-body localization (MBL). In higher dimensions, the existence of MBL is a delicate question due to the possibility of inclusions of lower dimensional ''thermal'' regions. In this talk, I will argue that MBL is stable in higher dimensions by analyzing the geometry of a MBL insulator coupled to a thermal edge and develop a phenomenology of such systems.
Many-body physics of ultracold doublet sigma molecules in optical lattices
NASA Astrophysics Data System (ADS)
Shchedrin, Gavriil; Jaschke, Daniel; Han, Wei; Carr, Lincoln D.; Green, Dermot G.; Aldegunde, Jesus; Hutson, Jeremy M.
2016-05-01
The creation of ultracold polar molecules provides a unique opportunity to discover and explore new regimes in strongly interacting many-body quantum systems. Polar molecules have strong long-range dipole-dipole interactions that allow one to realize exotic phenomena such as topological phases and quantum magnetism. We explore quantum many-body systems formed by molecules in doublet sigma (2 Σ) states, with both electric dipole moments and electron spin S = 1 / 2 , but without electronic orbital momentum. The Hamiltonian for doublet sigma molecules includes molecular rotation terms, spin-rotation interaction, hyperfine terms including both spin-spin and nuclear electric quadrupole interactions, and molecular dipole-dipole interactions. The complete control of the molecular quantum states can be accomplished by applying electric and magnetic fields to molecules trapped in optical lattices. We provide the complete theoretical treatment for experimentally relevant doublet sigma molecules such as SrF and CaF and discuss the associated single-body and many-body physics. Funded by AFOSR and NSF.
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
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.
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.
A rigorous result on many-body localization
NASA Astrophysics Data System (ADS)
Imbrie, John
The mathematical theory of many-body localization is in its infancy. Lack of thermalization is associated with the existence of a complete set of quasi-local integrals of motion. I will discuss a proof that a particular one-dimensional spin chain with random local interactions exhibits many-body localization. The proof depends on a physically reasonable assumption that limits the amount of level attraction in the system. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors. This provides an explicit construction of integrals of motion via convergent expansions.
Dynamical many-body localization in an integrable model
NASA Astrophysics Data System (ADS)
Keser, Aydin Cem; Ganeshan, Sriram; Refael, Gil; Galitski, Victor
2016-08-01
We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of "emergent" integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.
Particle-hole symmetry, many-body localization, and topological edge modes
NASA Astrophysics Data System (ADS)
Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.
We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).
Recent Progress in Many-Body Theories: Proceedings of the 12th International Conference
NASA Astrophysics Data System (ADS)
Carlson, Joseph A.; Ortiz, Gerardo
2006-07-01
Preface -- International advisory committee -- Feenberg medal session. Surface and superconductivity / L. P. Gor'kov. Spartak T. Belyaev - recipient of the Feenberg Medal / V. Zelevinsky. Many-body physics and spontaneous symmetry breaking / S. T. Belyaev -- Keynote speaker. The future lies ahead / P. W. Anderson -- Strongly correlated systems and phase transitions. Exact results for many-body problems using few-body methods / J. Cardy. Quantum matters: physics beyond Landau's paradigms / T. Senthil. Microscopic calculations of quantum phase transitions in frustrated magnetic lattices / R. F. Bishop & S. E. Krüger. Recent applications of the DMRG method / K. Hallberg. Functional renormalization group in the 2D Hubbard model / C. Honerkamp. Quantum phase transitions and event horizons: condensed matter analogies / G. Chapline. Spin-charge separation and topological phase transitions in Aharnov-Bohm rings of interacting electrons / B. Normand ... [et al.] -- Quantum fluids and solids. Two-particle-two-hole excitations in [symbol]He / E. Krotscheck, H. M. Böhm & K. Schörkhuber. Monolayer charged quantum films: a quantum simulation study / K. Wierschem & E. Manousakis. Can inconmensuration stabilize a superfluid phase of para-hydrogen? / M. Boninsegni. Analysis of the interatomic potential of the helium systems / S. Ujevic & S. A. Vitiello -- Nuclear physics and QCD. Quantum phase transitions in mesoscopic systems / F. Iachello. Nuclear-structure theory in the search for new fundamental physics / J. Engel. Matter at extreme density and its role in neutron stars and supernova / S. Reddy. New approaches to strong coupling lattice QCD / S. Chandrasekharan. Nuclear interactions from the renormalization group / A. Schwenk. Random interactions and ground state spin of finite Fermi systems / V. Zelevinsky & A. Volya -- Cold atoms and quantum information. Superfluid regimes in degenerate atomic fermi gases / G. V. Shlyapnikov. Bosons in optical lattices / S. L. Rolston
NASA Astrophysics Data System (ADS)
Masella, Michel; Cuniasse, Philippe
2003-07-01
A new model to study proteinic systems including a many-body polarization and a hydrogen bond energy contribution is presented. This model represents an extension of an earlier water many-body model [M. Masella and J.-P. Flament, J. Chem. Phys. 107 9105 (1997)]. As in this earlier model, the new model is developed to reproduce quantum computations on small molecular aggregates, and, in this first paper, we focus our efforts in developing an accurate potential to describe interactions among all nonbonded atoms occurring in proteins, and among those atoms and six cations of biological interest: Li+, Na+, K+, Mg2+, Ca2+, and Zn2+. Intramolecular degrees of freedom are described as in classical two-body force fields. In the present paper, the new model is applied to investigate the properties of small ion-neutral [M,Ln]m+ complexes and of small hydrogen-bonded systems. The results showed that this model is able to reproduce most of the theoretical quantum predictions and experimental data published until now regarding those systems.
Many-body physics via machine learning
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; von Lilienfeld, O. Anatole; Millis, Andrew J.
We demonstrate a method for the use of machine learning (ML) to solve the equations of many-body physics, which are functional equations linking a bare to an interacting Green's function (or self-energy) offering transferable power of prediction for physical quantities for both the forward and the reverse engineering problem of materials. Functions are represented by coefficients in an orthogonal polynomial expansion and kernel ridge regression is used. The method is demonstrated using as an example a database built from Dynamical Mean Field theory (DMFT) calculations on the three dimensional Hubbard model. We discuss the extension to a database for real materials. We also discuss some new area of investigation concerning high throughput predictions for real materials by offering a perspective of how our scheme is general enough for applications to other problems involving the inversion of integral equations from the integrated knowledge such as the analytical continuation of the Green's function and the reconstruction of lattice structures from X-ray spectra. Office of Science of the U.S. Department of Energy under SubContract DOE No. 3F-3138 and FG-ER04169.
Robustness of Many-Body Localization in the Presence of Dissipation.
Levi, Emanuele; Heyl, Markus; Lesanovsky, Igor; Garrahan, Juan P
2016-06-10
Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices. PMID:27341255
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
Interaction energies of large clusters from many-body expansion
NASA Astrophysics Data System (ADS)
Góra, Urszula; Podeszwa, Rafał; Cencek, Wojciech; Szalewicz, Krzysztof
2011-12-01
In the canonical supermolecular approach, calculations of interaction energies for molecular clusters involve a calculation of the whole cluster, which becomes expensive as the cluster size increases. We propose a novel approach to this task by demonstrating that interaction energies of such clusters can be constructed from those of small subclusters with a much lower computational cost by applying progressively lower-level methods for subsequent terms in the many-body expansion. The efficiency of such "stratified approximation" many-body approach (SAMBA) is due to the rapid convergence of the many-body expansion for typical molecular clusters. The method has been applied to water clusters (H2O)n, n = 6, 16, 24. For the hexamer, the best results that can be obtained with current computational resources in the canonical supermolecular method were reproduced to within about one tenth of the uncertainty of the canonical approach while using 24 times less computer time in the many-body expansion calculations. For (H_2 O)_{24}, SAMBA is particularly beneficial and we report interaction energies with accuracy that is currently impossible to obtain with the canonical supermolecular approach. Moreover, our results were computed using two orders of magnitude smaller computer resources than used in the previous best calculations for this system. We also show that the basis-set superposition errors should be removed in calculations for large clusters.
Robustness of Many-Body Localization in the Presence of Dissipation
NASA Astrophysics Data System (ADS)
Levi, Emanuele; Heyl, Markus; Lesanovsky, Igor; Garrahan, Juan P.
2016-06-01
Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system—an interacting fermionic chain subject to quenched disorder—in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.
On the simulation of indistinguishable fermions in the many-body Wigner formalism
Sellier, J.M. Dimov, I.
2015-01-01
The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.
Particle-hole symmetry, many-body localization, and topological edge modes
NASA Astrophysics Data System (ADS)
Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.
2016-04-01
We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: Even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the noninteracting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders.
On the simulation of indistinguishable fermions in the many-body Wigner formalism
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.
Exploring many-body physics with deep networks
NASA Astrophysics Data System (ADS)
Torlai, Giacomo; Carrasquilla, Juan; Schwab, David; Melko, Roger
The introduction of neural networks with deep architecture has led to a revolution, giving rise to a new wave of technologies empowering our modern society. Although data science has been the main focus, the idea of generic algorithms which automatically extract features and representations from raw data is quite general and applicable in multiple scenarios. Motivated by the effectiveness of deep learning algorithms in revealing complex patterns and structures underlying data, we are interested in exploiting such tool in the context of many-body physics. In this talk we will focus on how to extract information about the physics of a many-body system from the generative training of a deep network, and ultimately consider discriminative tasks, such as phase diagrams estimation and critical points detection. We will discuss results for different classical spin systems, including models with quenched disorder.
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.
Purification and many-body localization in cold atomic gases.
Andraschko, Felix; Enss, Tilman; Sirker, Jesko
2014-11-21
We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its nonequilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. Furthermore, we confirm as hallmarks of the many-body localized phase a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach; this allows us to perform the disorder average exactly, thus producing data without any statistical noise and with maximal simulation times of up to a factor 10 longer than in the clean case. PMID:25479517
Superadiabatic forces in Brownian many-body dynamics.
Fortini, Andrea; de Las Heras, Daniel; Brader, Joseph M; Schmidt, Matthias
2014-10-17
Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously difficult problem. For the case of classical Brownian many-body dynamics, we present a simulation method that allows us to isolate and precisely evaluate superadiabatic correlations and the resulting forces. Application of the method to a system of one-dimensional hard particles reveals the importance for the dynamics, as well as the complexity, of these nontrivial out-of-equilibrium contributions. Our findings help clarify the status of dynamical density functional theory and provide a rational basis for the development of improved theories. PMID:25361281
Superadiabatic Forces in Brownian Many-Body Dynamics
NASA Astrophysics Data System (ADS)
Fortini, Andrea; de las Heras, Daniel; Brader, Joseph M.; Schmidt, Matthias
2014-10-01
Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously difficult problem. For the case of classical Brownian many-body dynamics, we present a simulation method that allows us to isolate and precisely evaluate superadiabatic correlations and the resulting forces. Application of the method to a system of one-dimensional hard particles reveals the importance for the dynamics, as well as the complexity, of these nontrivial out-of-equilibrium contributions. Our findings help clarify the status of dynamical density functional theory and provide a rational basis for the development of improved theories.
Influence of dephasing on many-body localization
NASA Astrophysics Data System (ADS)
Medvedyeva, Mariya V.; Prosen, Tomaž; Žnidarič, Marko
2016-03-01
We study the effects of dephasing noise on a prototypical many-body localized system—the X X Z spin 1 /2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process.
Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.
Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E
2016-08-01
Adaptive quantum mechanical (QM)/molecular mechanical (MM) methods enable efficient molecular simulations of chemistry in solution. Reactive subregions are modeled with an accurate QM potential energy expression while the rest of the system is described in a more approximate manner (MM). As solvent molecules diffuse in and out of the reactive region, they are gradually included into (and excluded from) the QM expression. It would be desirable to model such a system with a single adaptive Hamiltonian, but thus far this has resulted in distorted structures at the boundary between the two regions. Solving this long outstanding problem will allow microcanonical adaptive QM/MM simulations that can be used to obtain vibrational spectra and dynamical properties. The difficulty lies in the complex QM potential energy expression, with a many-body expansion that contains higher order terms. Here, we outline a Hamiltonian adaptive multiscale scheme within the framework of many-body potentials. The adaptive expressions are entirely general, and complementary to all standard (nonadaptive) QM/MM embedding schemes available. We demonstrate the merit of our approach on a molecular system defined by two different MM potentials (MM/MM'). For the long-range interactions a numerical scheme is used (particle mesh Ewald), which yields energy expressions that are many-body in nature. Our Hamiltonian approach is the first to provide both energy conservation and the correct solvent structure everywhere in this system. PMID:27332140
NASA Astrophysics Data System (ADS)
Cuniasse, Philippe; Masella, Michel
2003-07-01
The origin of the interactions occurring in the calmodulin protein interacting with one of its target peptide and counterions, and binding four calcium dications, has been investigated in the gas phase, using the many-body model presented in Paper I [Masella and Cuniasse, J. Chem. Phys. 119, 1866 (2003)] and a classical pairwise force field. As compared to the latter force field, the many-body model is shown to provide a geometrical description of the calmodulin/target peptide structure in better agreement with the x-ray experimental one, and a better description of the Ca2+ binding sites (as compared to "small molecule" structures reported in the Cambridge Structural Database). Regarding the energy, both models provide qualitatively a similar description of the interactions occurring in the calmodulin/target peptide system. However, quantitatively, the pairwise model predicts interaction energies greater by about 25% as compared to the many-body one in the case of calmodulin/Ca2+ interactions. This is due to the inability of pairwise force fields to account for the strong anticooperative effects predicted to occur in [Ca,(carboxylate)n]2-n systems by both the many-body model and quantum computations. Hence, the new many-body model appears to be well suited for describing proteinic systems interacting with cations, both in terms of geometry and energy.
Machine learning for many-body physics: The case of the Anderson impurity model
NASA Astrophysics Data System (ADS)
Arsenault, Louis-François; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Millis, Andrew J.
2014-10-01
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are investigated; a representation in terms of Legendre polynomials is found to be superior due to its limited number of coefficients and its applicability to state of the art methods of solution. The dependence of the errors on the size of the training set is determined. The results indicate that a machine learning approach to dynamical mean-field theory may be feasible.
Charge optimized many-body potential for aluminum
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.
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.
NASA Astrophysics Data System (ADS)
Beugeling, W.; Andreanov, A.; Haque, Masudul
2015-02-01
In the spectrum of many-body quantum systems appearing in condensed matter physics, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of the full eigenspectrum has grown more recently, in particular in the context of non-equilibrium questions. Wave functions of interacting lattice quantum systems can be characterized either by local observables or by global properties such as the participation ratio (PR) in a many-body basis or the entanglement between various partitions. We present a study of the PR and of the entanglement entropy (EE) between two roughly equal spatial partitions of the system, in all the eigenfunctions of local Hamiltonians. Motivated by the similarity of the PR and EE—both are generically larger in the bulk and smaller near the edges of the spectrum—we quantitatively analyze the correlation between them. We elucidate the effect of (proximity to) integrability, showing how low-entanglement and low-PR states appear also in the middle of the spectrum as one approaches integrable points. We also determine the precise scaling behaviour of the eigenstate-to-eigenstate fluctuations of the PR and EE with respect to system size and characterize the statistical distribution of these quantities near the middle of the spectrum.
Cavity-Free Photon Blockade Induced by Many-Body Bound States
NASA Astrophysics Data System (ADS)
Zheng, Huaixiu; Gauthier, Daniel; Baranger, Harold
2012-02-01
We show theoretically that a variety of strong quantum nonlinear phenomena occur in a completely open one-dimensional waveguide coupled to an N-type four-level system. This system could be realized, for example, in experiments using superconducting circuits. We focus on photon blockade, photon-induced tunneling, bunching or anti-bunching, and the creation of single-photon states, all in the absence of a cavity. Many-body bound states appear due to the strong photon-photon correlation mediated by the four-level system. These bound states cause photon blockade, generating a sub-Poissonian single-photon source [1]. Such a source is crucial for quantum cryptography and distributed quantum networking; our work thus supports the notion that open quantum systems can play a critical role in the manipulation of individual, mobile quanta, a key goal of quantum communication. [1] H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. Lett. in press (2011), arXiv:1107.0309.
Scalable Dissipative Preparation of Many-Body Entanglement.
Reiter, Florentin; Reeb, David; Sørensen, Anders S
2016-07-22
We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives the system from an arbitrary initial state into a Greenberger-Horne-Zeilinger state. We demonstrate that using our technique highly entangled steady states can be prepared efficiently in a time that scales polynomially with the system size. Our protocol assumes generic couplings and will thus enable the dissipative production of multiparticle entanglement in a wide range of physical systems. As an example, we demonstrate the feasibility of our scheme in state-of-the-art trapped-ion systems. PMID:27494463
Scalable Dissipative Preparation of Many-Body Entanglement
NASA Astrophysics Data System (ADS)
Reiter, Florentin; Reeb, David; Sørensen, Anders S.
2016-07-01
We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives the system from an arbitrary initial state into a Greenberger-Horne-Zeilinger state. We demonstrate that using our technique highly entangled steady states can be prepared efficiently in a time that scales polynomially with the system size. Our protocol assumes generic couplings and will thus enable the dissipative production of multiparticle entanglement in a wide range of physical systems. As an example, we demonstrate the feasibility of our scheme in state-of-the-art trapped-ion systems.
Nonequilibrium many-body steady states via Keldysh formalism
NASA Astrophysics Data System (ADS)
Maghrebi, Mohammad F.; Gorshkov, Alexey V.
2016-01-01
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
Chiral Symmetry and Many-Body Effect in Multilayer Graphene
NASA Astrophysics Data System (ADS)
Hamamoto, Yuji; Kawarabayashi, Tohru; Aoki, Hideo; Hatsugai, Yasuhiro
2013-08-01
Influence of the chiral symmetry on the many-body problem in multilayer graphene in magnetic fields is investigated. For a spinless electron model on the honeycomb lattice the many-body ground state is shown to be a doubly-degenerate chiral condensate irrespective of the number of layers. The energy spectrum calculated numerically with the exact diagonalization method reveals for ABC-stacked multilayer graphenes that the many-body gap decreases monotonically with the number of layers.
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.
Vibrational relaxation in fluids: A many body scattering formalism
NASA Astrophysics Data System (ADS)
Dardi, Peter S.; Cukier, R. I.
1987-02-01
We derive an expression for the vibrational energy relaxation rate constant for dilute diatomic molecules in a structureless fluid. Our approach is based on a many-body scattering formalism within the Markov approximation. Using a quantum scattering formalism allows us to formally separate the inelastic part of the problem from the bath dynamics. We assume that the vibrational transition rate is small, and accordingly we treat the inelastic potential as a perturbation. Also, we assume that the translational motion of the diatom and the bath can be treated classically. The separation of the inelastic interaction from the bath dynamics allows the bath motion to be written in terms of a classical time correlation function of the bath density relative to the diatom. The bath, though, evolves under two Hamiltonians; one with the diatom in its initial state and the other with the diatom in its final state. A method is introduced to approximate this time correlation function in terms of single Hamiltonian correlation functions. We discuss the approximations inherent in our method and also those in the independent binary collision (IBC) model.
Long tail distributions near the many-body localization transition
NASA Astrophysics Data System (ADS)
Luitz, David J.
2016-04-01
The random field S =1/2 Heisenberg chain exhibits a dynamical many body localization transition at a critical disorder strength, which depends on the energy density. At weak disorder, the eigenstate thermalization hypothesis (ETH) is fulfilled on average, making local observables smooth functions of energy, whose eigenstate-to-eigenstate fluctuations decrease exponentially with system size. We demonstrate the validity of ETH in the thermal phase as well as its breakdown in the localized phase and show that rare states exist which do not strictly follow ETH, becoming more frequent closer to the transition. Similarly, the probability distribution of the entanglement entropy at intermediate disorder develops long tails all the way down to zero entanglement. We propose that these low entanglement tails stem from localized regions at the subsystem boundaries which were recently discussed as a possible mechanism for subdiffusive transport in the ergodic phase.
Higher-order renormalization of graphene many-body theory
NASA Astrophysics Data System (ADS)
González, J.
2012-08-01
We study the many-body theory of graphene Dirac quasiparticles interacting via the long-range Coulomb potential, taking as a starting point the ladder approximation to different vertex functions. We test in this way the low-energy behavior of the electron system beyond the simple logarithmic dependence of electronic correlators on the high-energy cutoff, which is characteristic of the large- N approximation. We show that the graphene many-body theory is perfectly renormalizable in the ladder approximation, as all higher powers in the cutoff dependence can be absorbed into the redefinition of a finite number of parameters (namely, the Fermi velocity and the weight of the fields) that remain free of infrared divergences even at the charge neutrality point. We illustrate this fact in the case of the vertex for the current density, where a complete cancellation between the cutoff dependences of vertex and electron self-energy corrections becomes crucial for the preservation of the gauge invariance of the theory. The other potentially divergent vertex corresponds to the staggered (sublattice odd) charge density, which is made cutoff independent by a redefinition in the scale of the density operator. This allows to compute a well-defined, scale invariant anomalous dimension to all orders in the ladder series, which becomes singular at a value of the interaction strength marking the onset of chiral symmetry breaking (and gap opening) in the Dirac field theory. The critical coupling we obtain in this way matches with great accuracy the value found with a quite different method, based on the resolution of the gap equation, thus reassuring the predictability of our renormalization approach.
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.
Accessing Rydberg-dressed interactions using many-body Ramsey dynamics
NASA Astrophysics Data System (ADS)
Mukherjee, Rick; Killian, Thomas; Hazzard, Kaden
2016-05-01
We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system. Our scheme operates comfortably within experimentally measured lifetimes, and accesses a regime where quantum superpositions are crucial. We build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, for which we derive an exact solution. Due to the structure of Rydberg interactions, the dynamics differs significantly from that in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results are relevant for the current ongoing experiments, including those at Rice University.
Extended slow dynamical regime close to the many-body localization transition
NASA Astrophysics Data System (ADS)
Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
2016-02-01
Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L =28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth S (t ) ∝t1 /z with a disorder-dependent exponent z ≥1 , in contrast with the pure ballistic growth z =1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t ) ∝t-ζ with a continuously varying disorder-dependent exponent ζ , vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.
Investigation of many-body forces in krypton and xenon
Salacuse, J.J.; Egelstaff, P.A.
1988-10-15
The simplicity of the state dependence at relatively high temperatures ofthe many-body potential contribution to the pressure and energy has been pointed out previously (J. Ram and P. A. Egelstaff, J. Phys. Chem. Liq. 14, 29 (1984); A. Teitsima and P. A. Egelstaff, Phys. Rev. A 21, 367 (1980)). In this paper, we investigate how far these many-body potential terms may be represented by simple models in the case of krypton on the 423-, 273-, 190-, and 150-K isotherms, and xenon on the 170-, 210-, and 270-K isotherms. At the higher temperatures the best agreement is found for the mean-field type of theory, and some consequences are pointed out. On the lower isotherms a state point is found where the many-body energy vanishes, and large departures from mean-field behavior are observed. This is attributed to the influence of short-ranged many-body forces.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
NASA Astrophysics Data System (ADS)
Hermes, Matthew R.; Hirata, So
2014-08-01
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm-1 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Hermes, Matthew R.; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Communication: Random phase approximation renormalized many-body perturbation theory
Bates, Jefferson E.; Furche, Filipp
2013-11-07
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.
Exploring the few- to many-body crossover using cold atoms in one dimension
NASA Astrophysics Data System (ADS)
Zinner, Nikolaj Thomas
2016-03-01
Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a 'cool' quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.
NASA Astrophysics Data System (ADS)
Lode, Axel U. J.; Chakrabarti, Barnali; Kota, Venkata K. B.
2015-09-01
We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of N =10 interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schrödinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a nontrivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that mean-field approaches such as the time-dependent Gross-Pitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (R-MCTDHB).
Understanding many-body physics in one dimension from the Lieb-Liniger model
NASA Astrophysics Data System (ADS)
Jiang, Yu-Zhu; Chen, Yang-Yang; Guan, Xi-Wen
2015-05-01
This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb-Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe’s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb-Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang-Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb-Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability. Project supported by the National Basic Research Program of China (Grant No. 2012CB922101) and the National Natural Science Foundation of China (Grant Nos. 11374331 and 11304357).
Fermionic Many-Body States Under the Microscope
NASA Astrophysics Data System (ADS)
Mazurenko, Anton; Greif, Daniel; Parsons, Maxwell F.; Chiu, Christie S.; Blatt, Sebastian; Huber, Florian; Ji, Geoffrey; Greiner, Markus
2016-05-01
We demonstrate the site-resolved observation of two component, fermionic Mott insulators, band insulators and metals of ultracold 6 Li in a single layer of a three-dimensional optical lattice. Site-resolved imaging enables measurements of local observables, including the local occupation variance. A comparison with predictions of the high temperature series expansion of the Fermi-Hubbard model is consistent with thermally equilibrated samples, with local entropies as low as 0 . 7kB per particle in the Mott insulator, and 0 . 5kB per particle in the band insulator. The phase diagram in the Mott regime is studied, exploiting the fact that the underlying harmonic potential enables measurements across a wide range of chemical potentials in a single experimental shot. Our experiments provide a starting point for implementing entropy redistribution based cooling schemes. Furthermore, we report on our recent progress towards measuring site-resolved spin correlations for low temperature samples, opening the door for studying many-body systems in theoretically intractable regimes. Current address: Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany.
Groundstatable fermionic wavefunctions and their associated many-body Hamiltonians
Charrier, Daniel Chamon, Claudio
2010-01-15
In the vast majority of many-body problems, it is the kinetic energy part of the Hamiltonian that is best known microscopically, and it is the detailed form of the interactions between the particles, the potential energy term, that is harder to determine from first principles. An example is the case of high temperature superconductors: while a tight-binding model captures the kinetic term, it is not clear that there is superconductivity with only an onsite repulsion and, thus, that the problem is accurately described by the Hubbard model alone. Here we pose the question of whether, once the kinetic energy is fixed, a candidate ground state is groundstatable or not. The easiness to answer this question is strongly related to the presence or the absence of a sign problem in the system. When groundstatability is satisfied, it is simple to obtain the potential energy that will lead to such a ground state. As a concrete case study, we apply these ideas to different fermionic wavefunctions with superconductive or spin-density wave correlations and we also study the influence of Jastrow factors. The kinetic energy considered is a simple nearest neighbor hopping term.
On the representation of many-body interactions in water
Medders, Gregory; Gotz, Andreas; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-09
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.
Many-body processes in atomic and molecular physics
Chu, Shih-I.
1990-02-01
This report discusses the following topics: Dynamics of Multiphoton Excitation in Rydberg Atoms; Nonlinear Schrodinger Equation and Dissipative Quantum Dynamics in Periodic Fields; Density Matrix Formulation of Complex Geometric Phases in Dissipative Systems; and A. C. Stark Shifts of Excited States of Atoms in Strong Fields.
Many-body localization and symmetry protected topology with ultracold Rydberg atoms
NASA Astrophysics Data System (ADS)
Potirniche, Ionut-Dragos; Schleier-Smith, Monika; Vishwanath, Ashvin; Yao, Norman
The interplay between quantum entanglement and symmetry-protected topological order has led to the classification of gapped, interacting, one dimensional quantum phases. A consequence of this classification is the existence of a diverse set of exactly solvable models, which serve as paradigmatic examples of various SPT orders. The experimental realization of such models has been hampered by the challenge of implementing tunable multi-body interactions. Recently, an alternate strategy has arisen: periodic driving. Indeed, it has been shown that the dynamics of a simple Floquet transverse-field Ising model can mirror that of the celebrated Haldane chain. However, as SPT order is expected only in the ground state while a driven system is expected to heat to infinite temperature, the ability to observe such ``Floquet'' SPT phases remains an open question. Here, we demonstrate that strong disorder, leading to many-body localization, stabilizes SPT order at finite energy densities while also preventing arbitrary heating of the system. Moreover, we propose a natural experimental implementation in a 1D optical lattice of ultracold Rydberg atoms.
Thermal Phase Transitions in Finite Quantum Systems
Dean, D.J.
2001-10-18
In this Proceedings, the author will describe the behavior of two different quantum-mechanical systems as a function of increasing temperature. While these systems are somewhat different, the questions addressed are very similar, namely, how does one describe transitions in phase of a finite many-body system; how does one recognize these transitions in practical calculations; and how may one obtain the order of the transition.
NASA Astrophysics Data System (ADS)
Hu, Hui; Wang, An-Bang; Yi, Su; Liu, Xia-Ji
2016-05-01
We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasiperiodic (bichromatic) optical lattice within a standard variational approach. We consider both repulsive and attractive contact interactions for such a simple many-body localization problem of Fermi polarons. The variational approach enables us to access relatively large systems and therefore may be used to understand many-body localization in the thermodynamic limit. The energy and wave function of the polaron states are found to be strongly affected by the quasirandom lattice potential and their experimental measurements (i.e., via radio-frequency spectroscopy or quantum gas microscope) therefore provide a sensitive way to underpin the localization transition. We determine a phase diagram by calculating two critical quasirandom disorder strengths, which correspond to the onset of the localization of the ground-state polaron state and the many-body localization of all polaron states, respectively. Our predicted phase diagram could be straightforwardly examined in current cold-atom experiments.
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
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.
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.
Combined coupled-cluster and many-body perturbation theories
NASA Astrophysics Data System (ADS)
Hirata, So; Fan, Peng-Dong; Auer, Alexander A.; Nooijen, Marcel; Piecuch, Piotr
2004-12-01
Various approximations combining coupled-cluster (CC) and many-body perturbation theories have been derived and implemented into the parallel execution programs that take into account the spin, spatial (real Abelian), and permutation symmetries and that are applicable to closed- and open-shell molecules. The implemented models range from the CCSD(T), CCSD[T], CCSD(2)T, CCSD(2)TQ, and CCSDT(2)Q methods to the completely renormalized (CR) CCSD(T) and CCSD[T] approaches, where CCSD (CCSDT) stands for the CC method with connected single and double (single, double, and triple) cluster operators, and subscripted or parenthesized 2, T, and Q indicate the perturbation order or the excitation ranks of the cluster operators included in the corrections. The derivation and computer implementation have been automated by the algebraic and symbolic manipulation program TENSOR CONTRACTION ENGINE (TCE). The TCE-synthesized subroutines generate the tensors with the highest excitation rank in a blockwise manner so that they need not be stored in their entirety, while enabling the efficient reuse of other precalculated intermediate tensors defined by prioritizing the memory optimization as well as operation minimization. Consequently, the overall storage requirements for the corrections due to connected triple and quadruple cluster operators scale as O(n4) and O(n6), respectively (n being a measure of the system size). For systems with modest multireference character of their wave functions, we found that the order of accuracy is CCSD
On the representation of many-body interactions in water
Medders, Gregory; Gotz, Andreas; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-09
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 ofmore » 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.« less
On the representation of many-body interactions in water
Medders, Gregory R.; Gotz, Andreas W.; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-09
Our recent work has shown that the many-body expansion of the interactionenergy can be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and long-range interactions at different orders is investigated by analyzing water potentials that treat the leading terms of the many-body expansion through implicit (i.e., TTM3-F and TTM4-F PESs) and explicit (i.e., WHBB and MB-pol PESs) representations. Moreover, it is found that explicit short-range representations of 2-body and 3-body interactions along with a physically correct incorporation of short- and long-range contributions are necessary for an accurate representationmore » of the waterinteractions from the gas to the condensed phase. Likewise, a complete many-body representation of the dipole moment surface is found to be crucial to reproducing the correct intensities of the infrared spectrum of liquid water.« less
Entangling qubit registers via many-body states of ultracold atoms
NASA Astrophysics Data System (ADS)
Melko, R. G.; Herdman, C. M.; Iouchtchenko, D.; Roy, P.-N.; Del Maestro, A.
2016-04-01
Inspired by the experimental measurement of the Rényi entanglement entropy in a lattice of ultracold atoms by Islam et al. [Nature (London) 528, 77 (2015), 10.1038/nature15750], we propose a method to entangle two spatially separated qubits using the quantum many-body state as a resource. Through local operations accessible in an experiment, entanglement is transferred to a qubit register from atoms at the ends of a one-dimensional chain. We compute the operational entanglement, which bounds the entanglement physically transferable from the many-body resource to the register, and discuss a protocol for its experimental measurement. Finally, we explore measures for the amount of entanglement available in the register after transfer, suitable for use in quantum information applications.
Many-body effects on adiabatic passage through Feshbach resonances
Tikhonenkov, I.; Pazy, E.; Band, Y. B.; Vardi, A.; Fleischhauer, M.
2006-04-15
We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms {gamma} on sweep rate {alpha}, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law {gamma}{proportional_to}{alpha} is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law {gamma}{proportional_to}{alpha}{sup 1/3} is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.
NASA Astrophysics Data System (ADS)
Kita, Takafumi; Takada, Yasutami
1990-09-01
A one-dimensional many-electron system with a repulsive δ-function interaction is studied by the application of the variational method developed in the preceding paper [Takada and Kita, Phys. Rev. A 42, 3242 (1990)] in order to illustrate its actual implementation. Our results on the grand potential, the entropy, and the specific heat are compared in detail with the exact ones that are calculated by the numerical solution of the coupled integral equations obtained by the Bethe ansatz.
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 Mean-Field Equations: Parallel implementation
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-12-31
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms.
Meson Structure in a Relativistic Many-Body Approach
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2000-02-07
Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, Tamm-Dancoff (TDA), and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion, and the meson spin, orbital, and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA. (c) 2000 The American Physical Society.
Levy distribution in many-particle quantum systems
Ponomarev, A. V.; Denisov, S.; Haenggi, P.
2010-04-15
The Levy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas - a one-dimensional gas of N impenetrable (hard-core) bosons-harmonically confined on a lattice at finite temperatures obeys a Levy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable Levy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.
Dynamical many-body phases of the parametrically driven, dissipative Dicke model
NASA Astrophysics Data System (ADS)
Chitra, R.; Zilberberg, O.
2015-08-01
Control and manipulation of quantum engineered systems allows for the utilization of time-dependent parametric modulations for accessing novel out-of-equilibrium phenomena. In the absence of such driving, the dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a parametric modulation of this coupling and discover a rich phase diagram as a function of the modulation strength. We find that in addition to the established normal and super-radiant phases, a new phase with pulsed superradiance, which we term dynamical normal phase, appears when the system is parametrically driven. Employing different methods, we characterize the different phases and the transitions between them. Specific heed is paid to the role of dissipation in determining the phase boundaries. Our analysis paves the road for the experimental study of dynamically stabilized phases of interacting light and matter.
Many-body Anderson localization in one-dimensional systems
NASA Astrophysics Data System (ADS)
Delande, Dominique; Sacha, Krzysztof; Płodzień, Marcin; Avazbaev, Sanat K.; Zakrzewski, Jakub
2013-04-01
We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The localization length of the particles' center of mass—computed analytically for weak disorder—is in good agreement with the quasi-exact numerical observations using the time evolving block decimation algorithm. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions.
Evolution of regulatory complexes: a many-body system
NASA Astrophysics Data System (ADS)
Nouemohammad, Armita; Laessig, Michael
2013-03-01
In eukaryotes, many genes have complex regulatory input, which is encoded by multiple transcription factor binding sites linked to a common function. Interactions between transcription factors and site complexes on DNA control the production of protein in cells. Here, we present a quantitative evolutionary analysis of binding site complexes in yeast. We show that these complexes have a joint binding phenotype, which is under substantial stabilizing selection and is well conserved within Saccharomyces paradoxus populations and between three species of Saccharomyces. At the same time, individual low-affinity sites evolve near-neutrally and show considerable affinity variation even within one population. Thus, functionality of and selection on regulatory complexes emerge from the entire cloud of sites, but cannot be pinned down to individual sites. Our method is based on a biophysical model, which determines site occupancies and establishes a joint affinity phenotype for binding site complexes. We infer a fitness landscape depending on this phenotype using yeast whole-genome polymorphism data and a new method of quantitative trait analysis. Our fitness landscape predicts the amount of binding phenotype conservation, as well as ubiquitous compensatory changes between sites in the cloud. Our results open a new avenue to understand the regulatory ``grammar'' of eukaryotic genomes based on quantitative evolution models. Carl-Icahn Laboratory, Washington Road, Princeton 08544 NJ
NASA Astrophysics Data System (ADS)
Burin, Alexander L.
2015-09-01
Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping V (R ) ∝R-α always leads to the localization breakdown in a thermodynamic limit of an infinite system at α <3 d /2 where d is a system dimension. The delocalization takes place due to the induced Ising interactions U (R ) ∝R-2 α of "extended" resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring α ≥2 d which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.
First-principles energetics of water clusters and ice: A many-body analysis
Gillan, M. J.; Alfè, D.; Bartók, A. P.; Csányi, G.
2013-12-28
Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
First-principles energetics of water clusters and ice: A many-body analysis
NASA Astrophysics Data System (ADS)
Gillan, M. J.; Alfè, D.; Bartók, A. P.; Csányi, G.
2013-12-01
Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
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-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation
NASA Astrophysics Data System (ADS)
Lindgren, I.; Salomonson, S.; Hedendahl, D.
2005-03-01
The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.
NASA Astrophysics Data System (ADS)
Wang, Huai-Yu; Jen, S. U.; Yu, Jing-Zhi
2006-03-01
In the treatment of Heisenberg Hamiltonian containing single-ion anisotropy by means of many-body Green’s function method, the decoupling of the anisotropy term in higher order Green’s functions usually takes an Anderson-Callen (AC) form. In this paper, possible improvement schemes of AC decoupling are discussed by comparison of the results with those of quantum Monte Carlo and frame rotation methods. We choose one scheme with a factor concerning the effect of the external field. Next, we discuss a possible difficulty of the frame rotation method in treating systems with single-ion anisotropies in more than one direction. Then we extended our method [Phys. Rev. B 70, 134424 (2004)] to treat magnetic films. Some magnetic properties of ultrathin ferromagnetic films with thicknesses up to 16 monolayers are studied. The properties investigated include transition point, effective anisotropy coefficient, field-induced magnetization reorientation, and hysteresis loop. Several cases are investigated for uniaxial anisotropy and external field along different directions. The transition point, the effective anisotropy coefficient, the coercivity, and the loop area increase with increasing film thickness. The coercivity decreases and the loop area reduces with increasing temperature. The hysteresis loop along field direction is different from that along easy-axis direction. The coercivity and the area of the loop obtained in the former case are larger than the latter case. The reasons are analyzed by investigation of the trajectory of magnetization in detail. The influence of dipole interaction on the magnetic properties is discussed.
Extended slow dynamical regime near the many-body localization transition
NASA Astrophysics Data System (ADS)
Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
Many-body localization is characterized by a slow logarithmic growth of entanglement entropy after a global quantum quench while the local memory of an initial spin imbalance remains at infinite time. We address the dynamics in the delocalized ergodic regime, where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibium dynamics of the random-field Heisenberg chain is studied up to L = 28 sites, starting from an initially unantangled high-energy product state. With such a global quench protocol, we study the time evolution of the entanglement entropy, as well as the spin density imbalance in order to make contact with recent cold atom experiments. Within most of the delocalized phase, we unambiguously find a sub-ballistic entanglement growth S (t) ~t 1 / z with a disorder-dependent exponent z >= 1 , in contrast with the pure ballistic growth z = 1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance I (t) ~t-ζ with a continuously varying disorder- dependent exponent ζ, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional metallic state where transport is sub-diffusive.
Many-body dispersion effects in the binding of adsorbates on metal surfaces
Maurer, Reinhard J.; Ruiz, Victor G.; Tkatchenko, Alexandre
2015-09-14
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic–inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate–surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches.
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
Strain Control of Fermiology and Many-Body Interactions in Two-Dimensional Ruthenates.
Burganov, B; Adamo, C; Mulder, A; Uchida, M; King, P D C; Harter, J W; Shai, D E; Gibbs, A S; Mackenzie, A P; Uecker, R; Bruetzam, M; Beasley, M R; Fennie, C J; Schlom, D G; Shen, K M
2016-05-13
Here we demonstrate how the Fermi surface topology and quantum many-body interactions can be manipulated via epitaxial strain in the spin-triplet superconductor Sr_{2}RuO_{4} and its isoelectronic counterpart Ba_{2}RuO_{4} using oxide molecular beam epitaxy, in situ angle-resolved photoemission spectroscopy, and transport measurements. Near the topological transition of the γ Fermi surface sheet, we observe clear signatures of critical fluctuations, while the quasiparticle mass enhancement is found to increase rapidly and monotonically with increasing Ru-O bond distance. Our work demonstrates the possibilities for using epitaxial strain as a disorder-free means of manipulating emergent properties, many-body interactions, and potentially the superconductivity in correlated materials. PMID:27232037
Strain Control of Fermiology and Many-Body Interactions in Two-Dimensional Ruthenates
NASA Astrophysics Data System (ADS)
Burganov, B.; Adamo, C.; Mulder, A.; Uchida, M.; King, P. D. C.; Harter, J. W.; Shai, D. E.; Gibbs, A. S.; Mackenzie, A. P.; Uecker, R.; Bruetzam, M.; Beasley, M. R.; Fennie, C. J.; Schlom, D. G.; Shen, K. M.
2016-05-01
Here we demonstrate how the Fermi surface topology and quantum many-body interactions can be manipulated via epitaxial strain in the spin-triplet superconductor Sr2RuO4 and its isoelectronic counterpart Ba2RuO4 using oxide molecular beam epitaxy, in situ angle-resolved photoemission spectroscopy, and transport measurements. Near the topological transition of the γ Fermi surface sheet, we observe clear signatures of critical fluctuations, while the quasiparticle mass enhancement is found to increase rapidly and monotonically with increasing Ru-O bond distance. Our work demonstrates the possibilities for using epitaxial strain as a disorder-free means of manipulating emergent properties, many-body interactions, and potentially the superconductivity in correlated materials.
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.
Charge-optimized many-body (COMB) potential for zirconium
NASA Astrophysics Data System (ADS)
Noordhoek, Mark J.; Liang, Tao; Lu, Zizhe; Shan, Tzu-Ray; Sinnott, Susan B.; Phillpot, Simon R.
2013-10-01
An interatomic potential for zirconium is developed within the charge-optimized many-body (COMB) formalism. The potential correctly predicts the hexagonal close-packed (HCP) structure as the ground state with cohesive energy, lattice parameters, and elastic constants matching experiment well. The most stable interstitial position is the basal octahedral followed by basal split, in agreement with recent first principles calculations. Stacking fault energies within the prism and basal planes satisfactorily match first principles calculations. A tensile test using nanocrystalline zirconium exhibits both prismatic {1 0 1bar 0}<1 1 2bar 0> slip and pyramidal {1 1 2bar 2}<1 1 2bar 3bar> slip, showing the model is capable of reproducing the mechanical deformation modes observed in experiments.
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.
Prethermalization and Many-body localization (MBL) in trapped ion spins
NASA Astrophysics Data System (ADS)
Zhang, J.; Smith, J.; Lee, A.; Hess, P. W.; Neyenhuis, B.; Richerme, P.; Hauke, P.; Heyl, M.; Huse, D. A.; Gong, Z. X.; Gorshkov, A.; Monroe, C.
2016-05-01
We present experimental investigations of quantum thermalization and equilibration dynamics in a precisely controlled, interacting, 171Yb+ spin chain, with up to 25 ions. We quench the trapped ion spins in a quantum many-body Hamiltonian with single-atom addressing techniques and measure the long-term dynamics with single-site resolution. With a long-range XY model spin Hamiltonian, we observe emergence of an exotic prethermal phase in the quench dynamics. This non-trivial prethermal phase arise from an inhomogeneous effective potential landscape, due to a combination of the long-range interactions and the open boundary condition. We also observe the absence of spin transport due to many-body localization (MBL) in the transverse-field Ising model with programmable disorder. We measure the Hamming distance and verify the growth of entanglement through the Quantum Fisher Information (QFI) entanglement witness, consistent with expectations for the MBL state. This work is supported by the ARO Atomic Physics Program, the AFOSR MURI on Quantum Measurement and Verification, and the NSF Physics Frontier Center at JQI.
NASA Astrophysics Data System (ADS)
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
Another New Solvable Many-Body Model of Goldfish Type
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2012-07-01
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'') featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion of an arbitrary number N of unit-mass point-particles in a plane. The N (generally complex) values z_{n}( t) at time t of the N coordinates of these moving particles are given by the N eigenvalues of a time-dependent N× N matrix U( t) explicitly known in terms of the 2N initial data z_{n}( 0) and dot{z}_{n}(0) . This model comes in two different variants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''); for other special values of these parameters this property holds up to corrections vanishing exponentially as t→ ∞ (''asymptotic isochrony''). Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.
Electron-phonon coupling using many-body GW theory
NASA Astrophysics Data System (ADS)
Monserrat, Bartomeu; Vanderbilt, David
Electron-phonon coupling drives a plethora of phenomena, such as superconductivity in metals, or the temperature dependence of optical properties in semiconductors. There is increasing evidence that semi-local density functional theory (DFT) is not adequate for the description of electron-phonon coupling, and instead effects such as electronic correlation need to be included. Unfortunately, methods beyond semi-local DFT are computationally demanding, limiting the study of these phenomena. In this talk we will introduce the idea of ``thermal lines'', which can be used to explore the vibrational phase space of solids and molecules at small computational cost. In particular, we will describe how thermal lines can be exploited to calculate the temperature dependence of band structures beyond semi-local DFT, by using many-body GW theory, or by including the effects of spin-orbit coupling. We will present first-principles results showing the effects of electron correlation on the strength of electron-phonon coupling, and the effects of electron-phonon coupling on topological states of matter. Supported by Robinson College, Cambridge, and the Cambridge Philosophical Society.
From Discrete Breathers to Many Body Localization and Flatbands
NASA Astrophysics Data System (ADS)
Flach, Sergej
Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.
Atomic many-body effects and Lamb shifts in alkali metals
NASA Astrophysics Data System (ADS)
Ginges, J. S. M.; Berengut, J. C.
2016-05-01
We present a detailed study of the radiative potential method [V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005), 10.1103/PhysRevA.72.052115], which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms and ions over the range 10 ≤Z ≤120 , where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s , p , and d waves over the series of alkali-metal atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many-body effects of core relaxation and second- and higher-order perturbation theory on the interaction of the valence electron with the core are calculated. The inclusion of many-body effects tends to increase the size of the shifts, with the enhancement particularly significant for d waves; for K to E119, the self-energy shifts for d waves are only an order of magnitude smaller than the s -wave shifts. It is shown that taking into account many-body effects is essential for an accurate description of the Lamb shift.
Approaching the complete-basis limit with a truncated many-body expansion.
Richard, Ryan M; Lao, Ka Un; Herbert, John M
2013-12-14
High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-ζ basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion-water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers. PMID:24329051
Approaching the complete-basis limit with a truncated many-body expansion
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2013-12-14
High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-ζ basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion–water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers.
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2016-07-01
For short-ranged disordered quantum models in one dimension, the many-body-localization is analyzed via the adaptation to the many-body context (Serbyn et al 2015 Phys. Rev. X 5 041047) of the Thouless point of view on the Anderson transition: the question is whether a local interaction between two long chains is able to reshuffle completely the eigenstates (delocalized phase with a volume-law entanglement) or whether the hybridization between tensor states remains limited (many-body-localized phase with an area-law entanglement). The central object is thus the level of hybridization induced by the matrix elements of local operators, as compared with the difference of diagonal energies. The multifractal analysis of these matrix elements of local operators is used to analyze the corresponding statistics of resonances. Our main conclusion is that the critical point is characterized by the strong-multifractality spectrum f(0≤slant α ≤slant 2)=\\fracα{2} , well known in the context of Anderson localization in spaces of effective infinite dimensionality, where the size of the Hilbert space grows exponentially with the volume. Finally, the possibility of a delocalized non-ergodic phase near criticality is discussed.
Many-body manifestation of interaction-free measurement: The Elitzur-Vaidman bomb
NASA Astrophysics Data System (ADS)
Zilberberg, Oded; Romito, Alessandro; Gefen, Yuval
2016-03-01
We consider an implementation of the Elitzur-Vaidman bomb experiment in a dc-biased electronic Mach-Zehnder interferometer with a leakage port on one of its arms playing the role of a "lousy bomb." Many-body correlations tend to screen out manifestations of interaction-free measurement. Analyzing the correlations between the current at the interferometer's drains and at the leakage port, we identify the limit where the originally proposed single-particle effect is recovered. Specifically, we find that in the regime of sufficiently diluted injected electron beam and short measurement times, effects of quantum-mechanical wave-particle duality emerge in the cross-current correlations.
Novel solvable extensions of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Calogero, F.; Iona, S.
2005-10-01
A novel solvable extension of the goldfish N-body problem is presented. Its Newtonian equations of motion read ζ̈n=2aζ\\dot nζn+2∑m =1,m≠nN(ζ\\dot n-aζn2)(ζ\\dot m-aζm2)/(ζn-ζm), n =1,…,N, where a is an arbitrary (nonvanishing) constant and the rest of the notation is self-evident. The isochronous version of this model is characterized by the Newtonian equations of motion ζ̈n-3iω\\zdot n-2ω2zn=2a(\\zdot n-iωzn)zn+2∑m =1,m≠nN(\\zdot n-iωzn-azn2)(\\zdot m-iωzm-azm2)/(zn-zm), n =1,…,N, where ω is an arbitrary positive constant and the points zn(t) move now necessarily in the complex z-plane. The generic solution of this second model is completely periodic with a period Tk=kT which is an integer multiple k (not larger than N!, indeed generally much smaller) of the basic period T =2π/ω and which is independent of the initial data (for sufficiently small, but otherwise arbitrary, changes of such data). These many-body models have an intriguing variety of equilibrium configurations (genuine: with no two particles sitting at the same place), but only for small values of N (N =2,3,4 for the first model, N =2,3,4,5 for the second). Other versions of these models are also discussed. The study of the behavior of the second, isochronous model around its equilibrium configurations yields some amusing diophantine results.
NASA Astrophysics Data System (ADS)
Kang, Nam; Ryu, Jai; Choi, Sang
1998-07-01
Utilizing state-independent projection operators, we present a new optical conductivity formula for cyclotron transition in the system of electrons interacting anisotropically with phonons. The line-shape factor appearing in the conductivity tensor contains the many body effects for electrons and phonons. Applying this formula, we determine the two deformation potentials (dilation potential Ξd and uniaxial shear potential Ξu) of Ge in the quantum limit. By fitting the present theoretical values with the experimental data of Murase, Enjouji and Otsuka [J. Phys. Soc. Jpn. 29 (1970) 1248] and Kobori, Ohyama and Otsuka [J. Phys. Soc. Jpn. 59 (1990) 2141], we obtain Ξu=17.0±0.6 eV and Ξd=-10.88±0.47 eV.
1/f Fluctuation and a Many-Body Disk Model of Slip Phenomena
NASA Astrophysics Data System (ADS)
Hirata, Takayuki
1999-10-01
A many-body disk system was investigated as a model of slip phenomena. A two-dimensional many-body disk system was used as a model of the boundary layer between slip surfaces. Frustrated states occurred in this system depending on the disk configuration. Experiments with this were carried out using a random packing configuration (packing fraction: 0.74 ˜0.76). Acrylic resin disks were packed between a co-axial outer rotating cylinder and an inner fixed cylinder. The outer cylinder was rotated by a motor and the torque at the fixed inner cylinder was measured in a time series. Stick-slip and 1/f fluctuation were observed in the time series.
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
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 S{sub N}2 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
Dielectric many-body effects in arrays of charged cylindrical macromolecules
NASA Astrophysics Data System (ADS)
Sinkovits, Daniel W.; Barros, Kipton; Dobnikar, Jure; Kandu&{Caron; C}, Matej; Naji, Ali; Podgornik, Rudolf; Luijten, Erik
2012-02-01
Nonuniform dielectric constants are a ubiquitous aspect of condensed-matter systems, but nevertheless widely ignored in simulations. Analytical work suggests that the polarization effects resulting from these inhomogeneities can produce many-body interactions that qualitatively alter the behavior of systems driven by electrostatic interactions, but such work relies on approximations. Recently, we have developed an algorithm that computes the fluctuating polarization charge at the interface between dielectric materials during a molecular dynamics simulation, without approximation. Here, we apply this approach to investigate arrays of charged cylindrical macromolecules in the presence of explicit counterions. We study the dielectric many-body effects as a function of separation, dielectric constant variation, and counterion valency. Our findings have implications for the aggregation of polyelectrolytes such as F-actin or DNA.
NASA Astrophysics Data System (ADS)
Carmele, Alexander; Heyl, Markus; Kraus, Christina; Dalmonte, Marcello
2015-11-01
We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occurring in the bulk. In particular, for pure loss dynamics we find a universal exponent α ≃2 /3 . We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.
Cesium Ultra-Long-Range Rydberg Molecules and Many-Body Physics
NASA Astrophysics Data System (ADS)
Yang, Jin; Jahangiri, Akbar; Rittenhouse, Seth; Reschke, Margarita; Booth, Donald; Sadeghpour, Hossein; Shaffer, James
2016-05-01
Ultra-long-range Rydberg molecules have received increasing interest recently because of their novel properties such as the ability to serve as an electron trap, the potential to possess kilo-Debye dipole moments, and their unique binding mechanism. Recently, experiments focusing on Rydberg P-state and D-state molecules have revealed interesting new features of these novel molecules, like coupling between singlet and triplet scattering channels, p-wave scattering dominated states and their behavior in magnetic fields. In this presentation, we report our recent observation of Cesium D-state ultra-long-range Rydberg molecules and compare our observations to theoretical calculations. We also report our preliminary data on ``polymer'' molecules, which are formed by one Cs Rydberg atom but more than one Cs ground state atom. The transition from a few-body system to a many-body system can provide insight into many-body physics. We acknowledge funding from the NSF.
Simulations of dipolar fluids using effective many-body isotropic interactions.
Sindt, Julien O; Camp, Philip J
2015-07-14
The partition function of a system with pairwise-additive anisotropic dipole-dipole interactions is equal to that of a hypothetical system with many-body isotropic interactions [G. Stell, Phys. Rev. Lett. 32, 286 (1974)]. The effective many-body interactions contain n-body contributions of all orders. Each contribution is known as an expansion in terms of the particle-particle distances r, and the coefficients are temperature dependent. The leading-order two-body term is the familiar -r(-6) attraction, and the leading-order three-body term is equivalent to the Axilrod-Teller interaction. In this work, a fluid of particles with the leading-order two-body and three-body interactions is compared to an equivalent dipolar soft-sphere fluid. Molecular simulations are used to determine the conditions under which the effective many-body interactions reproduce the fluid-phase structures of the dipolar system. The effective many-body interaction works well at moderately high temperatures but fails at low temperatures where particle chaining is expected to occur. It is shown that an adjustment of the coefficients of the two-body and three-body terms leads to a good description of the structure of the dipolar fluid even in the chaining regime, due primarily to the ground-state linear configuration of the three-body Axilrod-Teller interaction. The vapor-liquid phase diagrams of systems with different Axilrod-Teller contributions are determined. As the strength of the three-body interaction is increased, the critical temperature and density both decrease and disappear completely above a threshold strength, where chaining eventually suppresses the condensation transition. PMID:26178112
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/ .
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.
Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition
NASA Astrophysics Data System (ADS)
Devakul, Trithep; Singh, Rajiv
We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies. Work based on Phys. Rev. Lett. 115, 187201.
Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition
NASA Astrophysics Data System (ADS)
Devakul, Trithep; Singh, Rajiv R. P.
2015-10-01
We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.
Quantum entanglement in condensed matter systems
NASA Astrophysics Data System (ADS)
Laflorencie, Nicolas
2016-08-01
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial information can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contain key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in detail. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.
TRIQS: A toolbox for research on interacting quantum systems
NASA Astrophysics Data System (ADS)
Parcollet, Olivier; Ferrero, Michel; Ayral, Thomas; Hafermann, Hartmut; Krivenko, Igor; Messio, Laura; Seth, Priyanka
2015-11-01
We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it.
Keldysh field theory for driven open quantum systems.
Sieberer, L M; Buchhold, M; Diehl, S
2016-09-01
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems. PMID:27482736
Keldysh field theory for driven open quantum systems
NASA Astrophysics Data System (ADS)
Sieberer, L. M.; Buchhold, M.; Diehl, S.
2016-09-01
Recent experimental developments in diverse areas—ranging from cold atomic gases to light-driven semiconductors to microcavity arrays—move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven–dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
NASA Astrophysics Data System (ADS)
Monthus, Cécile
2016-03-01
A fully many-body localized (FMBL) quantum disordered system is characterized by the emergence of an extensive number of local conserved operators that prevents the relaxation towards thermal equilibrium. These local conserved operators can be seen as the building blocks of the whole set of eigenstates. In this paper, we propose to construct them explicitly via block real-space renormalization. The principle is that each renormalization group step diagonalizes the smallest remaining blocks and produces a conserved operator for each block. The final output for a chain of N spins is a hierarchical organization of the N conserved operators with ≤ft(\\frac{\\ln N}{\\ln 2}\\right) layers. The system size nature of the conserved operators of the top layers is necessary to describe the possible long-range order of the excited eigenstates and the possible critical points between different FMBL phases. We discuss the similarities and the differences with the strong disorder RSRG-X method that generates the whole set of the 2 N eigenstates via a binary tree of N layers. The approach is applied to the long-range quantum spin-glass Ising model, where the constructed excited eigenstates are found to be exactly like ground states in another disorder realization, so that they can be either in the paramagnetic phase, in the spin-glass phase or critical.
Impact of many-body correlations on the dynamics of an ion-controlled bosonic Josephson junction
NASA Astrophysics Data System (ADS)
Schurer, J. M.; Gerritsma, R.; Schmelcher, P.; Negretti, A.
2016-06-01
We investigate an atomic ensemble of interacting bosons trapped in a symmetric double-well potential in contact with a single tightly trapped ion which has been recently proposed [R. Gerritsma et al., Phys. Rev. Lett. 109, 080402 (2012), 10.1103/PhysRevLett.109.080402] as a source of entanglement between a Bose-Einstein condensate and an ion. Compared to the previous study, the present work aims at performing a detailed and accurate many-body analysis of such a combined atomic quantum system by means of the ab initio multiconfiguration time-dependent Hartree method for bosons, which allows us to take into account all correlations in the system. The analysis elucidates the importance of quantum correlations in the bosonic ensemble and reveals that entanglement generation between an ion and a condensate is indeed possible, as previously predicted. Moreover, we provide an intuitive picture of the impact of the correlations on the out-of-equilibrium dynamics by employing a natural orbital analysis which we show to be indeed experimentally verifiable.
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
Laser from a many-body correlated medium
NASA Astrophysics Data System (ADS)
Mascarenhas, Eduardo; Gerace, Dario; Flayac, Hugo; Santos, Marcelo F.; Auffèves, Alexia; Savona, Vincenzo
2016-05-01
We consider a nonequilibrium system of interacting emitters described by the XXZ model, whose excitonic transitions are spatially and spectrally coupled to a single mode cavity. We demonstrate that the output radiation field is sensitive to an interplay between the hopping (J ) and the interactions (U ) of the excitons. Moderate values of the short-ranged interaction are shown to induce laser with maximal output at the Heisenberg point (U =J ). In the laser regime, charge-charge correlations emerge and they are shown to strongly depend on the interaction-hopping ratio. In particular, the system shows charge-density correlations below the Heisenberg point and ferromagnetic correlations beyond the Heisenberg point. This contrast to the equilibrium behavior of the XXZ chain occurs since the laser explores highly excited states of the emitters.
Possible experimental manifestations of the many-body localization
NASA Astrophysics Data System (ADS)
Basko, D. M.; Aleiner, I. L.; Altshuler, B. L.
2007-08-01
Recently, it was predicted that if all one-electron states in a noninteracting disordered system are localized, the interaction between electrons in the absence of coupling to phonons leads to a finite-temperature metal-insulator transition. Here, we show that even in the presence of a weak coupling to phonons the transition manifests itself (i) in the nonlinear conduction, leading to a bistable I-V curve, and (ii) by a dramatic enhancement of the nonequilibrium current noise near the transition.
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.
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→ ∞.
Sorting quantum systems efficiently
NASA Astrophysics Data System (ADS)
Ionicioiu, Radu
2016-05-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation.
Sorting quantum systems efficiently.
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) - which direct photons according to their polarization - and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Sorting quantum systems efficiently
Ionicioiu, Radu
2016-01-01
Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation. PMID:27142705
Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
NASA Astrophysics Data System (ADS)
Li, Xiaopeng; Pixley, J. H.; Deng, Dong-Ling; Ganeshan, Sriram; Das Sarma, S.
2016-05-01
We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are studied by comparing entanglement and thermal entropy, and by calculating the scaling of subsystem particle-number fluctuations, respectively. We establish a nonergodic extended phase as a generic intermediate phase (between purely ergodic extended and nonergodic localized phases) for the many-body localization transition of noninteracting fermions where the entanglement entropy manifests a volume law (hence, "extended"), but there are large fluctuations in the subsystem particle numbers (hence, "nonergodic"). Based on the numerical results, we expect such an intermediate phase scenario may continue to hold even for the many-body localization in the presence of interactions as well. We find for many-body fermionic states in noninteracting one-dimensional Aubry-André and three-dimensional Anderson models that the entanglement entropy density and the normalized particle-number fluctuation have discontinuous jumps at the localization transition where the entanglement entropy is subthermal but obeys the "volume law." In the vicinity of the localization transition, we find that both the entanglement entropy and the particle-number fluctuations obey a single parameter scaling based on the diverging localization length. We argue using numerical and theoretical results that such a critical scaling behavior should persist for the interacting many-body localization problem with important observable consequences. Our work provides persuasive evidence in favor of there being two transitions in many-body systems with single-particle mobility edges, the first one indicating a transition from the purely localized nonergodic many-body localized phase to a nonergodic extended many-body metallic phase, and the second one being a transition
Hilbert-space localization in closed quantum systems
NASA Astrophysics Data System (ADS)
Cohen, Doron; Yukalov, Vyacheslav I.; Ziegler, Klaus
2016-04-01
Quantum localization within an energy shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space Anderson localization and its many-body Fock-space version. We use the term Hilbert-space localization in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state and on the strength of the many-body interactions using a recursive projection method.
Quantum coherence and correlations in quantum system
Xi, Zhengjun; Li, Yongming; Fan, Heng
2015-01-01
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem. PMID:26094795
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 1.68m0 and a Bohr radius of 2 Å. The results of this study hold the promise for potential applications of the GeC hybrid in optoelectronics.
Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice
NASA Astrophysics Data System (ADS)
Yi, W.; Diehl, S.; Daley, A. J.; Zoller, P.
2012-05-01
We discuss the preparation of many-body states of cold fermionic atoms in an optical lattice via controlled dissipative processes induced by coupling the system to a reservoir. Based on a mechanism combining Pauli blocking and phase locking between adjacent sites, we construct complete sets of jump operators describing coupling to a reservoir that leads to dissipative preparation of pairing states for fermions with various symmetries in the absence of direct inter-particle interactions. We discuss the uniqueness of these states, and demonstrate it with small-scale numerical simulations. In the late-time dissipative dynamics, we identify a ‘dissipative gap’ that persists in the thermodynamic limit. This gap implies exponential convergence of all many-body observables to their steady-state values. We then investigate how these pairing states can be used as a starting point for the preparation of the ground state of the Fermi-Hubbard Hamiltonian via an adiabatic state preparation process also involving the parent Hamiltonian of the pairing state. We also provide a proof-of-principle example for implementing these dissipative processes and the parent Hamiltonians of the pairing states, based on 171Yb atoms in optical lattice potentials.
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
Particle-hole configuration interaction and many-body perturbation theory: Application to Hg+
NASA Astrophysics Data System (ADS)
Berengut, J. C.
2016-07-01
The combination of configuration interaction and many-body perturbation theory methods is extended to nonperturbatively include configurations with electron holes below the designated Fermi level, allowing us to treat systems where holes play an important role. For example, the method can treat valence-hole systems like Ir17 +, particle-hole excitations in noble gases, and difficult transitions such as the 6 s →5 d-16 s2 optical clock transition in Hg+. We take the latter system as our test case for the method and obtain very good accuracy (˜1 %) for the low-lying transition energies. The α dependence of these transitions is calculated and used to reinterpret the existing best laboratory limits on the time dependence of the fine-structure constant.
Controlling many-body states by the electric-field effect in a two-dimensional material.
Li, L J; O'Farrell, E C T; Loh, K P; Eda, G; Özyilmaz, B; Castro Neto, A H
2016-01-14
To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially
Controlling many-body states by the electric-field effect in a two-dimensional material
NASA Astrophysics Data System (ADS)
Li, L. J.; O'Farrell, E. C. T.; Loh, K. P.; Eda, G.; Özyilmaz, B.; Castro Neto, A. H.
2016-01-01
To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially
Quantum statistical ensemble for emissive correlated systems.
Shakirov, Alexey M; Shchadilova, Yulia E; Rubtsov, Alexey N
2016-06-01
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of the transitions induced by the interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in the vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of the stable eigenstates. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N-particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in the different sectors, in contrast to the Gibbs ensemble. We investigate the transition rates between the eigenstates to understand the emergence of the Boltzmann distribution and find their exponential dependence on the transition energy. We argue that this property of transition rates is generic for a wide class of emissive quantum many-body systems. PMID:27415223
Quantum statistical ensemble for emissive correlated systems
NASA Astrophysics Data System (ADS)
Shakirov, Alexey M.; Shchadilova, Yulia E.; Rubtsov, Alexey N.
2016-06-01
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of the transitions induced by the interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in the vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of the stable eigenstates. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N -particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in the different sectors, in contrast to the Gibbs ensemble. We investigate the transition rates between the eigenstates to understand the emergence of the Boltzmann distribution and find their exponential dependence on the transition energy. We argue that this property of transition rates is generic for a wide class of emissive quantum many-body systems.
Quantum electromechanical systems
NASA Astrophysics Data System (ADS)
Milburn, Gerard J.; Polkinghorne, Rodney
2001-11-01
We discuss the conditions under which electromechanical systems, fabricated on a sub micron scale, require a quantum description. We illustrate the discussion with the example of a mechanical electroscope for which the resonant frequency of a cantilever changes in response to a local charge. We show how such devices may be used as a quantum noise limited apparatus for detection of a single charge or spin with applications to quantum computing.
Demerdash, Omar; Head-Gordon, Teresa
2016-08-01
We analyze convergence of energies and forces for the AMOEBA classical polarizable model when evaluated as a many-body expansion (MBE) against the corresponding N-body parent potential in the context of a condensed-phase water simulation. This is in contrast to most MBE formulations based on quantum mechanics, which focus only on convergence of energies for gas-phase clusters. Using a single water molecule as a definition of a body, we find that truncation of the MBE at third order, 3-AMOEBA, captures direct polarization exactly and yields apparent good convergence of the mutual polarization energy. However, it renders large errors in the magnitude of polarization forces and requires at least fourth-order terms in the MBE to converge toward the parent potential gradient values. We can improve the convergence of polarization forces for 3-AMOEBA by embedding the polarization response of dimers and trimers within a complete representation of the fixed electrostatics of the entire system. We show that the electrostatic embedding formalism helps identify the specific configurations involving linear hydrogen-bonding arrangements that are poorly convergent at the 3-body level. By extending the definition of a body to be a large water cluster, we can reduce errors in forces to yield an approximate polarization model that is up to 10 times faster than the parent potential. The 3-AMOEBA model offers new ways to investigate how the properties of bulk water depend on the degree of connectivity in the liquid. PMID:27405002
Photon-dressed quasiparticle states in 1D and 2D materials: a many-body Floquet approach
NASA Astrophysics Data System (ADS)
Manghi, Franca; Puviani, Matteo
We studiy the interplay between electron-electron interactions and non-equilibrium conditions associated to time-dependent external fields. Exploring phases of quantum matter away from equilibrium may give access to regimes inaccessible under equilibrium conditions. What makes this field particularly interesting is the possibility to engineer new phases of matter by an external tunable control. We have developed a scheme that allows to treat photo-induced phenomena in the presence of electron-electron many body interactions, where both the nonlinear effects of the external field and the electron-electron correlation are treated simultaneously and in a non-perturbative way. The Floquet approach is used to include the effects of the external time periodic field, and the Cluster Perturbation Theory to describe interacting electrons in a lattice. They are merged in a Floquet-Green function method that allows to calculate photon dressed quasiparticle excitation. For 1D systems we show that an unconventional Mott insulator-to-metal transition occurs for given characteristics of the applied field (intensity and frequency). The method has also been applied to the 2D honeycomb lattice (graphene), where in the presence of realistic values of electron-electron interaction, we show that linearly polarized light may give rise to non-dissipative edge states associated to a non-trivial topological behavior.
NASA Astrophysics Data System (ADS)
Ginges, J. S. M.; Berengut, J. C.
2016-05-01
We calculate vacuum polarization corrections to the binding energies in neutral alkali atoms Na through to the superheavy element E119. We employ the relativistic Hartree–Fock method to demonstrate the importance of relaxation of the electronic core and the correlation potential method to study the effects of second and higher orders of perturbation theory. These many-body effects are sizeable for all orbitals, though particularly important for orbitals with angular momentum quantum number l\\gt 0. The orders of magnitude enhancement for d waves produces shifts that, for Rb and the heavier elements, are larger than those for p waves and only an order of magnitude smaller than the s-wave shifts. The many-body enhancement mechanisms that operate for vacuum polarization apply also to the larger self-energy corrections.
Entanglement in algebraic quantum mechanics: Majorana fermion systems
NASA Astrophysics Data System (ADS)
Benatti, F.; Floreanini, R.
2016-07-01
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.
Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid.
Dóra, Balázs; Pollmann, Frank; Fortágh, József; Zaránd, Gergely
2013-07-26
We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry. PMID:23931387
Many-body processes in black and gray matter-wave solitons
NASA Astrophysics Data System (ADS)
Krönke, Sven; Schmelcher, Peter
2015-05-01
We perform a comparative beyond-mean-field study of black and gray solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized density-engineering potential is developed and employed together with phase imprinting to cleanly initialize gray solitons. By means of ab initio simulations with the multiconfiguration time-dependent Hartree method for bosons, we demonstrate that quantum fluctuations limit the lifetime of the soliton contrast, which increases with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of gray solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analyzed in detail. Finally, the role of phase imprinting for the many-body dynamics is illuminated and additional nonlocal correlations in pairs of counterpropagating gray solitons are observed.
An exacting transition probability measurement - a direct test of atomic many-body theories
Dutta, Tarun; De Munshi, Debashis; Yum, Dahyun; Rebhi, Riadh; Mukherjee, Manas
2016-01-01
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P3/2 level of the barium ion, with precision below 0.5%. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition probabilities of low-lying excited states with a precision better than 1%. Furthermore, enhancing our understanding of the barium puzzle in barium stars requires branching fraction data for proper modelling of nucleo-synthesis. Our measurements are the first to provide a direct test of quantum many-body calculations on the barium ion with a precision below one percent and more importantly with no known systematic uncertainties. The unique measurement protocol proposed here can be easily extended to any decay with more than two channels and hence paves the way for measuring the branching fractions of other hydrogenic atoms with no significant systematic uncertainties. PMID:27432734
Many-body physics in the classical-field description of a degenerate Bose gas
Wright, T. M.; Davis, M. J.; Proukakis, N. P.
2011-08-15
The classical-field formalism has been widely applied in the calculation of normal correlation functions, and the characterization of condensation, in finite-temperature Bose gases. Here we discuss the extension of this method to the calculation of more general correlations, including the so-called anomalous correlations of the field, without recourse to symmetry-breaking assumptions. Our method is based on the introduction of U(1)-symmetric classical-field variables analogous to the modified quantum ladder operators of number-conserving approaches to the degenerate Bose gas, and allows us to rigorously quantify the anomalous and non-Gaussian character of the field fluctuations. We compare our results for anomalous correlation functions with the predictions of mean-field theories, and demonstrate that the nonlinear classical-field dynamics incorporate a full description of many-body processes which modify the effective mean-field potentials experienced by condensate and noncondensate atoms. We discuss the role of these processes in shaping the condensate mode, and thereby demonstrate the consistency of the Penrose-Onsager definition of the condensate orbital in the classical-field equilibrium. We consider the contribution of various noncondensate-field correlations to the overall suppression of density fluctuations and interactions in the field, and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase.
An exacting transition probability measurement - a direct test of atomic many-body theories
NASA Astrophysics Data System (ADS)
Dutta, Tarun; de Munshi, Debashis; Yum, Dahyun; Rebhi, Riadh; Mukherjee, Manas
2016-07-01
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P3/2 level of the barium ion, with precision below 0.5%. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition probabilities of low-lying excited states with a precision better than 1%. Furthermore, enhancing our understanding of the barium puzzle in barium stars requires branching fraction data for proper modelling of nucleo-synthesis. Our measurements are the first to provide a direct test of quantum many-body calculations on the barium ion with a precision below one percent and more importantly with no known systematic uncertainties. The unique measurement protocol proposed here can be easily extended to any decay with more than two channels and hence paves the way for measuring the branching fractions of other hydrogenic atoms with no significant systematic uncertainties.
An exacting transition probability measurement - a direct test of atomic many-body theories.
Dutta, Tarun; De Munshi, Debashis; Yum, Dahyun; Rebhi, Riadh; Mukherjee, Manas
2016-01-01
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P3/2 level of the barium ion, with precision below 0.5%. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition probabilities of low-lying excited states with a precision better than 1%. Furthermore, enhancing our understanding of the barium puzzle in barium stars requires branching fraction data for proper modelling of nucleo-synthesis. Our measurements are the first to provide a direct test of quantum many-body calculations on the barium ion with a precision below one percent and more importantly with no known systematic uncertainties. The unique measurement protocol proposed here can be easily extended to any decay with more than two channels and hence paves the way for measuring the branching fractions of other hydrogenic atoms with no significant systematic uncertainties. PMID:27432734
Field-Theoretical Approach to Many-Body Perturbation Theory: Combining MBPT and QED
Lindgren, Ingvar; Salomonson, Sten; Hedendahl, Daniel
2007-12-26
Many-Body Perturbation Theory (MBPT) is today highly developed. The electron correlation of atomic and molecular systems can be evaluated to essentially all orders of perturbation theory--also relativistically (RMBPT)--by means of techniques of Coupled-Cluster type. When high accuracy is needed, effects beyond RMBPT will enter, i.e., effects of retarded Breit interaction and of radiative effects (Lamb shift), effects normally referred to as QED effects. These effects can be evaluated by means of special techniques, like S-matrix formulation, which cannot simultaneously treat electron correlation. It would for many applications be desirable to have access to a numerical technique, where effects of electron correlation and of QED could be treated on the same footing. Such a technique is presently being developed and gradually implemented at our laboratory. Some numerical results will be given.
Electronic excitations of bulk LiCl from many-body perturbation theory
Jiang, Yun-Feng; Wang, Neng-Ping; Rohlfing, Michael
2013-12-07
We present the quasiparticle band structure and the optical excitation spectrum of bulk LiCl, using many-body perturbation theory. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, electron-hole pair states and optical excitations are obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function. The calculated band gap is 9.5 eV, which is in good agreement with the experimental result of 9.4 eV. And the calculated optical absorption spectrum, which contains an exciton peak at 8.8 eV and a resonant-exciton peak at 9.8 eV, is also in good agreement with experimental data.
Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry
NASA Astrophysics Data System (ADS)
Knap, Michael; Kantian, Adrian; Giamarchi, Thierry; Bloch, Immanuel; Lukin, Mikhail D.; Demler, Eugene
2013-10-01
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.
Many body effects study of electronic & optical properties of silicene-graphene hybrid
NASA Astrophysics Data System (ADS)
Drissi, L. B.; Ramadan, F. Z.
2015-04-01
Using first principles many-body calculations method, we study electronic and optical properties of 2D silicene-graphene hybrid. Based on phonon-spectrum calculations, we show the absence of soft modes indicating the stability of the system. We also calculate the band gap in both the absence and the presence of quasiparticle corrections. The analysis of optical absorption spectra and the correlation in real space between the excited electron-hole states reveals that the excitonic effects in silicene-graphene hybrid are significant and leads to strong bound excitons. The first active exciton is characterized by a binding energy of 0.81 eV, an effective mass 0.41m0 and a Bohr radius of 2.78 Å. The results of this work make silicene-graphene hybrid a promising candidate for optoelectronic applications.
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.
NASA Astrophysics Data System (ADS)
Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep; Huse, David A.
2016-06-01
We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed-point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.
The fixed hypernode method for the solution of the many body Schroedinger equation
Pederiva, F; Kalos, M H; Reboredo, F; Bressanini, D; Guclu, D; Colletti, L; Umrigar, C J
2006-01-24
We propose a new scheme for an approximate solution of the Schroedinger equation for a many-body interacting system, based on the use of pairs of walkers. Trial wavefunctions for these pairs are combinations of standard symmetric and antisymmetric wavefunctions. The method consists in applying a fixed-node restriction in the enlarged space, and computing the energy of the antisymmetric state from the knowledge of the exact ground state energy for the symmetric state. We made two conjectures: first, that this fixed-hypernode energy is an upper bound to the true fermion energy; second that this bound would necessarily be lower than the usual fixed-node energy using the same antisymmetric trial function. The first conjecture is true, and is proved in this paper. The second is not, and numerical and analytical counterexamples are given. The question of whether the fixed-hypernode energy can be better than the usual bound remains open.
NASA Astrophysics Data System (ADS)
Karrasch, C.; Moore, J. E.
2015-09-01
We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over 104 samples for lattices as large as 105 sites. We identify regimes in which non-Ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In the presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.
Colloquium: Non-Markovian dynamics in open quantum systems
NASA Astrophysics Data System (ADS)
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
Many-body microhydrodynamics of colloidal particles with active boundary layers
NASA Astrophysics Data System (ADS)
Singh, Rajesh; Ghose, Somdeb; Adhikari, R.
2015-06-01
Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one
NASA Astrophysics Data System (ADS)
Dušek, Miloslav; Haderka, Ondřej; Hendrych, Martin; Myška, Robert
1999-07-01
A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and sequences are ``refueled'' from a shared provably secret key transferred through the quantum channel. Two identification protocols are devised. The first protocol can be applied when legitimate users have an unjammable public channel at their disposal. The deception probability is derived for the case of a noisy quantum channel. The second protocol employs unconditionally secure authentication of information sent over the public channel, and thus can be applied even in the case when an adversary is allowed to modify public communications. An experimental realization of a quantum identification system is described.
The dimensionality reduction at surfaces as a playground for many-body and correlation effects
NASA Astrophysics Data System (ADS)
Tejeda, A.; Michel, E. G.; Mascaraque, A.
2013-03-01
Low-dimensional systems have always deserved attention due to the peculiarity of their physics, which is different from or even at odds with three-dimensional expectations. This is precisely the case for many-body effects, as electron-electron correlation or electron-phonon coupling are behind many intriguing problems in condensed matter physics. These interesting phenomena at low dimensions can be studied in one of the paradigms of two dimensionality—the surface of crystals. The maturity of today's surface science techniques allows us to perform thorough experimental studies that can be complemented by the current strength of state-of-the-art calculations. Surfaces are thus a natural two-dimensional playground for studying correlation and many-body effects, which is precisely the object of this special section. This special section presents a collection of eight invited articles, giving an overview of the current status of selected systems, promising techniques and theoretical approaches for studying many-body effects at surfaces and low-dimensional systems. The first article by Hofmann investigates electron-phonon coupling in quasi-free-standing graphene by decoupling graphene from two different substrates with different intercalating materials. The following article by Kirschner deals with the study of NiO films by electron pair emission, a technique particularly well-adapted for studying high electron correlation. Bovensiepen investigates electron-phonon coupling via the femtosecond time- and angle-resolved photoemission spectroscopy technique. The next article by Malterre analyses the phase diagram of alkalis on Si(111):B and studies the role of many-body physics. Biermann proposes an extended Hubbard model for the series of C, Si, Sn and Pb adatoms on Si(111) and obtains the inter-electronic interaction parameters by first principles. Continuing with the theoretical studies, Bechstedt analyses the influence of on-site electron correlation in insulating
Exact many-body ground states of a spin-1 Bose gas in Tonks-Girardeau limit
NASA Astrophysics Data System (ADS)
Jen, Hsiang-Hua; Yip, Sungkit
2016-05-01
We investigate the many-body ground states of a one-dimensional spin-1 Bose gas in Tonks-Girardeau (TG) limit. It is known that in TG gas limit of scalar bosons, the system becomes fermionized that bosons do not penetrate each other, and their wavefunctions take the form of noninteracting fermions. For a spin-1 Bose gas with an infinite atom-atom interaction in a harmonic trap, we construct the many-body ground states from the ones of a noninteracting Fermi gas along with the spin degrees of freedom. With zero magnetic field in the sector of Sz = 0 and in the regime of spin-incoherent Luttinger liquid where we assume negligible | a2 -a0 | , the interaction energy becomes spin-independent, and the many-body wavefunctions of a spin-1 Bose gas is also SU(3) invariant. The many-body wavefunction can be derived by calculating the weightings of spin functions using the conjugacy class G of SN symmetric group for the number of atoms N. We then study the first-order correlation function of the density matrix, from which we extract its momentum distribution. Finite-temperature calculation of the wavefunction by including orbital excitations is also investigated to compare with the case of spinless bosons. Ministry of Science and Technology, Taiwan, under Grant Number MOST-101-2112-M-001-021-MY3.
Quantum phase transitions in frustrated magnetic systems
NASA Astrophysics Data System (ADS)
Wölfle, P.; Schmitteckert, P.
2015-07-01
We review our recent work on quantum phase transitions in frustrated magnetic systems. In the first part a Pseudo Fermion Functional Renormalization Group (PFFRG) method is presented. By using an exact representation of spin 1/2 operators in terms of pseudofermions a quantum spin Hamiltonian may be mapped onto an interacting fermion system. For the latter an FRG treatment is employed. The results for the J1-J2 model and similar models of frustrated interaction show phase diagrams in agreement with those obtained by other methods, but give more detailed information on the nature of correlations, in particular in the non-magnetic phases. Applications of PFFRG to geometrically frustrated systems and to highly anisotropic Kitaev type models are also reported. In the second part the derivation of quantum spin models from the microscopic many-body Hamiltonian is discussed. The results for multiband systems with strong spin-orbit interaction encountered in the iridates class of compounds are shown to resolve some of the questions posed by experiment.
Vibrational modes in the quantum Hall system
NASA Astrophysics Data System (ADS)
Wooten, Rachel; Yan, Bin; Daily, Kevin; Greene, Chris H.
The hyperspherical adiabatic technique is more familiar to atomic and nuclear few-body systems, but can also be applied with high accuracy to the many-body quantum Hall problem. This technique reformulates the Schrödinger equation for N electrons into hyperspherical coordinates, which, after extracting the trivial center of mass, describes the system in terms of a single global size coordinate known as the hyperradius R, and 2 N - 3 remaining internal angular coordinates. The solutions are approximately separable in the hyperradial coordinate, and solutions in the system are found by treating the hyperradius as an adiabatic coordinate. The approximate separability of the wave functions in this coordinate suggests the presence of hyperradial vibrational modes which are not described in conventional theories. The vibrationally excited states share the internal geometry of their quantum Hall ground states, and their excitation frequencies may vary with the number of participating particles or the strength of the confinement. We plan to discuss the features of these vibrational modes and their possible detection in quantum Hall systems. NSF.
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.
The Hubbard dimer: a density functional case study of a many-body problem.
Carrascal, D J; Ferrer, J; Smith, J C; Burke, K
2015-10-01
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2. PMID:26380948
Applications of many-body physics to relativistic heavy ion collisions
NASA Astrophysics Data System (ADS)
Fillion-Gourdeau, Francois
In this dissertation, many-body physics techniques are used to study and improve ideas related to the description of heavy ion collisions at very high energy. The first part of the thesis concerns the production of tensor mesons in proton-proton (pp) collisions. An effective theory where the f2 meson couples to the energy-momentum tensor is proposed and a comparison of the inclusive cross-section computed in the collinear factorization, the k⊥-factorization and the color glass condensate is performed. A study of the phenomenology in pp collisions then shows a strong dependence on the parametrization of the unintegrated distribution function. The conclusion is that f2 meson production can be utilized to improve the understanding of the proton wave-function. In the second part, a similar investigation is performed by analysing the production cross-section of the eta' meson in pp and proton-nucleus (pA) collisions. The nucleus and proton are described by the CGC and the k⊥ -factorization respectively. A new technique for the computation of Wilson lines---color charge densities correlators in the McLerran-Venugopalan model is developped. The phenomenology shows that the cross-section in pA collisions is very sensitive to the value of the saturation scale, a crucial ingredient of the CGC picture. In the third part of the thesis, the collision term of the Boltzmann equation is derived from first principles at all orders and for any number of participating particles, starting from the full out-of-equilibrium quantum field theory and using the multiple scattering expansion. Finally, the emission of photons from a non-abelian strong classical field is investigated. A formalism based on Schwinger-Keldysh propagators relating the production rate of photons to the retarded solution of the Dirac equation in a background field is presented.
The Hubbard dimer: a density functional case study of a many-body problem
NASA Astrophysics Data System (ADS)
Carrascal, D. J.; Ferrer, J.; Smith, J. C.; Burke, K.
2015-10-01
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green’s function, demonstrating the ‘failure’ of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.
Electronic conduction properties of indium tin oxide: single-particle and many-body transport.
Lin, Juhn-Jong; Li, Zhi-Qing
2014-08-27
Indium tin oxide (Sn-doped In2O3-δ or ITO) is a very interesting and technologically important transparent conducting oxide. This class of material has been extensively investigated for decades, with research efforts mostly focusing on the application aspects. The fundamental issues of the electronic conduction properties of ITO from room temperature down to liquid-helium temperatures have rarely been addressed thus far. Studies of the electrical-transport properties over a wide range of temperature are essential to unravelling the underlying electronic dynamics and microscopic electronic parameters. In this topical review, we show that one can learn rich physics in ITO material, including the semi-classical Boltzmann transport, the quantum-interference electron transport, as well as the many-body Coulomb electron-electron interaction effects in the presence of disorder and inhomogeneity (granularity). To fully reveal the numerous avenues and unique opportunities that the ITO material has provided for fundamental condensed matter physics research, we demonstrate a variety of charge transport properties in different forms of ITO structures, including homogeneous polycrystalline thin and thick films, homogeneous single-crystalline nanowires and inhomogeneous ultrathin films. In this manner, we not only address new physics phenomena that can arise in ITO but also illustrate the versatility of the stable ITO material forms for potential technological applications. We emphasize that, microscopically, the novel and rich electronic conduction properties of ITO originate from the inherited robust free-electron-like energy bandstructure and low-carrier concentration (as compared with that in typical metals) characteristics of this class of material. Furthermore, a low carrier concentration leads to slow electron-phonon relaxation, which in turn causes the experimentally observed (i) a small residual resistance ratio, (ii) a linear electron diffusion thermoelectric power in
Many-body and spin-orbit aspects of the alternating current phenomena
NASA Astrophysics Data System (ADS)
Glenn, Rachel M.
The thesis reports on research in the general field of light interaction with matter. According to the topics addressed, it can be naturally divided into two parts: Part I, many-body aspects of the Rabi oscillations which a two-level systems undergoes under a strong resonant drive; and Part II, absorption of the ac field between the spectrum branches of two-dimensional fermions that are split by the combined action of Zeeman and spin-orbit (SO) fields. The focus of Part I is the following many-body effects that modify the conventional Rabi oscillations: Chapter 1, coupling of a two-level system to a single vibrational mode of the environment. Chapter 2, correlated Rabi oscillations in two electron-hole systems coupled by tunneling with strong electron-hole attraction. In Chapter 1, a new effect of Rabi-vibronic resonance is uncovered. If the frequency of the Rabi oscillations, OR, is close to the frequency o0 of the vibrational mode, the oscillations acquire a collective character. It is demonstrated that the actual frequency of the collective oscillations exhibits a bistable behavior as a function of OR - o0. The main finding in Chapter 2 is, that the Fourier spectrum of the Rabi oscillations in two coupled electron-hole systems undergoes a strong transformation with increasing O R. For OR smaller than the tunneling frequency, the spectrum is dominated by a low-frequency (<< OR ) component and contains two additional weaker lines; conventional Rabi oscillations are restored only as OR exceeds the electron-hole attraction strength. The highlight of Part II is a finding that, while the spectrum of absorption between either Zeeman-split branches or SO-split branches is close to a delta-peak, in the presence of both, it transforms into a broad line with singular behavior at the edges. In particular, when the magnitudes of Zeeman and SO are equal, absorption of very low (much smaller than the splitting) frequencies become possible. The shape of the absorption spectrum
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
NASA Astrophysics Data System (ADS)
Zhang, Xi; Zhang, Jin-Si; Shi, Ya-Zhou; Zhu, Xiao-Long; Tan, Zhi-Jie
2016-03-01
Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elusive many-body effect is attributed to ion-binding which is sensitive to ion concentration, ion valence, number of nanoparticles and charges on nanoparticles.
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
Applications of fidelity measures to complex quantum systems.
Wimberger, Sandro
2016-06-13
We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space. PMID:27140967
A many-body Hamiltonian for nanoparticles immersed in a polymer solution.
Woodward, Clifford E; Forsman, Jan
2015-01-13
We developed an analytical theory for the many-body potential of mean force (POMF) between N spheres immersed in a continuum chain fluid. The theory is almost exact for a Θ polymer solution in the protein limit (small particles, long polymers), where N-body effects are important. Polydispersity in polymer length according to a Schulz-Flory distribution emerges naturally from our analysis, as does the transition to the monodisperse limit. The analytical expression for the POMF allows for computer simulations employing the complete N-body potential (i.e., without n-body truncation; n < N). These are compared with simulations of an explicit particle/polymer mixture. We show that the theory produces fluid structure in excellent agreement with the explicit model simulations even when the system is strongly fluctuating, e.g., at or near the spinodal region. We also demonstrate that other commonly used theoretical approaches, such as truncation of the POMF at the pair level or the Asakura Oosawa model, are extremely inaccurate for these systems. PMID:25547161
Propagation of disturbances in degenerate quantum systems
NASA Astrophysics Data System (ADS)
Chancellor, Nicholas; Haas, Stephan
2011-07-01
Disturbances in gapless quantum many-body models are known to travel an unlimited distance throughout the system. Here, we explore this phenomenon in finite clusters with degenerate ground states. The specific model studied here is the one-dimensional J1-J2 Heisenberg Hamiltonian at and close to the Majumdar-Ghosh point. Both open and periodic boundary conditions are considered. Quenches are performed using a local magnetic field. The degenerate Majumdar-Ghosh ground state allows disturbances which carry quantum entanglement to propagate throughout the system and thus dephase the entire system within the degenerate subspace. These disturbances can also carry polarization, but not energy, as all energy is stored locally. The local evolution of the part of the system where energy is stored drives the rest of the system through long-range entanglement. We also examine approximations for the ground state of this Hamiltonian in the strong field limit and study how couplings away from the Majumdar-Ghosh point affect the propagation of disturbances. We find that even in the case of approximate degeneracy, a disturbance can be propagated throughout a finite system.
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.
Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems.
Cohen, Guy; Gull, Emanuel; Reichman, David R; Millis, Andrew J
2015-12-31
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. PMID:26765013
New Canonical Transformations to Eliminate External Fields in Quantum Many-Body Problems
Fujita, M.; Anma, D.; Fukuda, T.; Toyoda, T.; Koizumi, H.
2004-04-30
The wave function of an electron in a time varying electric field, a static magnetic field and a impurity potential can be transformed to the wave function of an electron without the electric field. By a unitary transformation, the electric field can be rigorously eliminated.
Exactness of wave functions from two-body exponential transformations in many-body quantum theory
Mazziotti, David A.
2004-01-01
Recent studies have considered the possibility that the exact ground-state wavefunction from any Hamiltonian with two-particle interactions may be generated from a single finite two-body exponential transformation acting on an arbitrary Slater determinant [Piecuch et al., Phys. Rev. Lett. 90, 113001 (2003)]. Using the Campbell-Baker-Hausdorff relation, we show that it is difficult for the variational minimum of this trial wave function to satisfy the contracted Schroedinger equation which is a necessary and sufficient condition for the wave function to satisfy the Schroedinger equation. A counterexample is presented through the Lipkin quasispin model with 4-50 fermions. When the number of fermions exceeds four, the wave function from a finite two-body exponential transformation is shown to be inexact. If the trial wave function ansatz is extended to include products of finite two-body exponential transformations acting on an arbitrary Slater-determinant reference, then we show that the ansatz includes the exact ground-state wave function from any Hamiltonian with only two-particle interactions. Connections between the two-body exponential transformation of the wave function and recent research on two-body exponential similarity transformations of the Hamiltonian [S.R. White, J. Chem. Phys. 117, 7472 (2002)] are discussed.
NASA Astrophysics Data System (ADS)
Kaminski, Adam
Angle Resolved Photoemission Spectroscopy (ARPES) is an experimental technique that has greatly contributed to our understanding of the electronic structure of the High Temperature Superconductors (HTSC). Over the last few years, it has provided vital information about the electronic structure, the Fermi Surface, gap anisotropy and it's temperature dependence, and a new phenomena known as the pseudogap. In this thesis we apply Angle Resolved Photoemission Spectroscopy to the study of electronic interactions in High Temperature Superconductors. The experimental portion of this thesis comprises three main areas, (i) participation in the construction of a new undulator beamline at the Synchrotron Radiation Center-Madison, Wisconsin, (ii) construction of a new ARPES system and (iii) collection and analysis of the data. The experimental results include precise determination of the Fermi Surface in BISCO 2212 and 2201, first observation of intrinsic ARPES lineshape at the nodal point of the Fermi Surface in BISCO 2212, detailed quantitative study of many body interactions along the nodal direction in normal and superconductive state, precise doping dependence analysis of the lineshape at the antinode.
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.
An Introductory Guide to GREEN’S Function Methods in Nuclear Many-Body Problems
NASA Astrophysics Data System (ADS)
Kuo, T. T. S.; Tzeng, Yiharn
We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.
Dynamical conductivity and its fluctuations along the crossover to many-body localization
NASA Astrophysics Data System (ADS)
Barišić, Osor S.; Kokalj, Jure; Balog, Ivan; Prelovšek, Peter
2016-07-01
We present a numerical study of the many-body localization (MBL) phenomenon in the high-temperature limit within an anisotropic Heisenberg model with random local fields. Taking the dynamical spin conductivity σ (ω ) as the test quantity, we investigate the full frequency dependence of sample-to-sample fluctuations and their scaling properties as a function of the system size L ≤28 and the frequency resolution. We identify differences between the general interacting case Δ >0 and the anisotropy Δ =0 , the latter corresponding to the standard Anderson localization. Except for the extreme MBL case when the relative sample-to-sample fluctuations became large, numerical results allow for the extraction of the low-ω dependence of the conductivity. Results for the dc value σ0 indicate a crossover into the MBL regime, i.e., an exponential-like variation with the disorder strength W . For the same regime, our numerical analysis indicates that the low-frequency exponent α exhibits a small departure from α ˜1 only.
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.
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language. PMID:27088565
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
NASA Astrophysics Data System (ADS)
Gogolin, Christian; Eisert, Jens
2016-05-01
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
NASA Astrophysics Data System (ADS)
Schröder, Florian A. Y. N.; Chin, Alex W.
2016-02-01
We report the development of an efficient many-body algorithm for simulating open quantum system dynamics that utilizes a time-dependent variational principle for matrix product states to evolve large system-environment states. Capturing all system-environment correlations, we reproduce the nonperturbative, quantum-critical dynamics of the zero-temperature spin-boson model, and then exploit the many-body information to visualize the complete time-frequency spectrum of the environmental excitations. Our "environmental spectra" reveal correlated vibrational motion in polaronic modes which preserve their vibrational coherence during incoherent spin relaxation, demonstrating how environment information could yield valuable insights into complex quantum dissipative processes.
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.
Non-Perturbative Many-Body Approach to the Hubbard Model and Single-Particle Pseudogap
NASA Astrophysics Data System (ADS)
Vilk, Y. M.; Tremblay, A.-M. S.
1997-11-01
A new approach to the single-band Hubbard model is described in the general context of many-body theories. It is based on enforcing conservation laws, the Pauli principle and a number of crucial sum-rules. More specifically, spin and charge susceptibilities are expressed, in a conserving approximation, as a function of two irreducible vertices whose values are found by imposing the local Pauli principle <~ngle n^2_\\uparrowrangle = <~ngle n_\\uparrowrangle as well as the local-moment sum-rule and consistency with the equations of motion in a local-field approximation. The Mermin-Wagner theorem in two dimensions is automatically satisfied. The effect of collective modes on single-particle properties is then obtained by a paramagnon-like formula that is consistent with the two-particle properties in the sense that the potential energy obtained from Tr Σ G is identical to that obtained using the fluctuation-dissipation theorem for susceptibilities. Since there is no Migdal theorem controlling the effect of spin and charge fluctuations on the self-energy, the required vertex corrections are included. It is shown that the theory is in quantitative agreement with Monte Carlo simulations for both single-particle and two-particle properties. The theory predicts a magnetic phase diagram where magnetic order persists away from half-filling but where ferromagnetism is completely suppressed. Both quantum-critical and renormalized-classical behavior can occur in certain parameter ranges. It is shown that in the renormalized classical regime, spin fluctuations lead to precursors of antiferromagnetic bands (shadow bands) and to the destruction of the Fermi-liquid quasiparticles in a wide temperature range above the zero-temperature phase transition. The upper critical dimension for this phenomenon is three. The analogous phenomenon of pairing pseudogap can occur in the attractive model in two dimensions when the pairing fluctuations become critical. Simple analytical expressions
Incorporating many-body effects into modeling of semiconductor lasers and amplifiers
Ning, C.Z.; Moloney, J.V.; Indik, R.A.
1997-06-01
Major many-body effects that are important for semiconductor laser modeling are summarized. The authors adopt a bottom-up approach to incorporate these many-body effects into a model for semiconductor lasers and amplifiers. The optical susceptibility function ({Chi}) computed from the semiconductor Bloch equations (SBEs) is approximated by a single Lorentzian, or a superposition of a few Lorentzians in the frequency domain. Their approach leads to a set of effective Bloch equations (EBEs). The authors compare this approach with the full microscopic SBEs for the case of pulse propagation. Good agreement between the two is obtained for pulse widths longer than tens of picoseconds.
Relativistic multireference many-body perturbation theory calculations on Au64+ - Au69+ ions
Vilkas, M J; Ishikawa, Y; Trabert, E
2006-03-31
Many-body perturbation theory (MBPT) calculations are an adequate tool for the description of the structure of highly charged multi-electron ions and for the analysis of their spectra. They demonstrate this by way of a re-investigation of n=3, {Delta}n=0 transitions in the EUV spectra of Na-, Mg-, Al-like, and Si-like ions of Au that have been obtained previously by heavy-ion accelerator based beam-foil spectroscopy. They discuss the evidence and propose several revisions on the basis of the multi-reference many-body perturbation theory calculations of Ne- through P-like ions of Au.
Curtright, Thomas; Mezincescu, Luca
2007-09-15
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+{nu}){sup 2}+{sigma}{sub k>0}{mu}{sub k} exp(ikx). In some nontrivial cases, equivalent Hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.
NASA Astrophysics Data System (ADS)
Dobnikar, J.; Rzehak, R.; von Grünberg, H. H.
2003-03-01
The solid-liquid phase diagram of charge-stabilized colloidal suspensions has been calculated using a technique that combines a continuous Poisson-Boltzmann description for the microscopic electrolyte ions with a molecular-dynamics simulation for the macroionic colloidal spheres. While correlations between the microions are neglected in this approach, many-body interactions between the colloids, mediated by the screening ionic fluid between them, are fully included. The Lindemann criterion has been used to determine the solid-to-liquid transition temperature in a colloidal system at a relatively high colloid volume fraction where many-body interactions are expected to be strong. With a view to the Derjaguin-Landau-Verwey-Overbeek theory predicting that colloids interact via Yukawa pair potentials, we compare our results with the phase diagram of a simple Yukawa liquid. We find an agreement under high-salt conditions, but considerable differences at low ionic strength. Using effective force calculations and data from molecular-dynamics simulations with simple model potentials, we further demonstrate that these differences are due to many-body interactions.
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
NASA Astrophysics Data System (ADS)
Freeman, Walter J.; Vitiello, Giuseppe
2006-06-01
Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Patterns form through interactions in both directions, so that the impact of transmitter molecule release can be analyzed to larger scales through synapses, dendrites, neurons, populations and brain systems to behavior, and control of that release can be described step-wise through transforms to smaller scales. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body physics by using tools that physicists have devised to analyze comparable hierarchies in other fields of science. We focus on a mesoscopic level that offers a multi-step pathway between the microscopic functions of neurons and the macroscopic functions of brain systems revealed by hemodynamic imaging. We use electroencephalographic (EEG) records collected from high-density electrode arrays fixed on the epidural surfaces of primary sensory and limbic areas in rabbits and cats trained to discriminate conditioned stimuli (CS) in the various modalities. High temporal resolution of EEG signals with the Hilbert transform gives evidence for diverse intermittent spatial patterns of amplitude (AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize in the beta and gamma ranges in very short time lags over very long distances. The dominant mechanism for neural interactions by axodendritic synaptic transmission should impose distance-dependent delays on the EEG oscillations owing to finite propagation velocities and sequential synaptic delays. It does not. EEGs show evidence for anomalous dispersion: neural populations have a low velocity range of information and energy transfers, and a high velocity range of the spread of phase transitions. This distinction labels the phenomenon but does not explain it. In this report we analyze these phenomena using concepts of energy dissipation, the maintenance by cortex of