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.
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.
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
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.
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
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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
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.
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
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.
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.
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.
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
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.
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.
Measuring entanglement entropies in many-body systems
Klich, Israel; Refael, Gil; Silva, Alessandro
2006-09-15
We explore the relation between entanglement entropy of quantum many-body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that, in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, XY spin chain, and chains with strong randomness.
Critical quasienergy states in driven many-body systems
NASA Astrophysics Data System (ADS)
Bastidas, 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.
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.
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.
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.
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.
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
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.
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
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).
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.
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).
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.
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
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-integrable
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.
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.
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.
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.
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
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
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.
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
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.
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.
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
. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Treatment of two particles reactions and decays. For each particle, calculation of the time measured in the particle reference frame, according to the instantaneous velocity. Possibility to dynamically add particle properties (spin, isospin, etc.), and reactions/decays, using a specific XML input file. Basic support for Monte Carlo simulations. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, “clusterization map”, and energy conservation precision test. As an example of use, we implemented a toy-model for nuclear relativistic collisions at 4.5 A GeV/c. Reasons for new version: Following our goal of applying chaos theory to nuclear relativistic collisions at 4.5 A GeV/c, we developed a reaction module integrated with the Chaos Many-Body Engine. In the previous version, inheriting the Particle class was the only possibility of implementing more particle properties (spin, isospin, and so on). In the new version, particle properties can be dynamically added using a dictionary object. The application was improved in order to calculate the time measured in the own reference frame of each particle. two particles reactions: a+b→c+d, decays: a→c+d, stimulated decays, more complicated schemas, implemented as various combinations of previous reactions. Following our goal of creating a flexible application, the reactions list, including the corresponding properties (cross sections, particles lifetime, etc.), could be supplied as parameter, using a specific XML configuration file. The simulation output files were modified for systems with reactions, assuring also the backward compatibility. We propose the “Clusterization Map” as a new investigation method of many-body systems. The multi-dimensional Lyapunov Exponent was adapted in order to be used for systems
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
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.
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.
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.
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
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
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.
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
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.
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.
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.
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.
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
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.
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.
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)
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.
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.
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
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
A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating meeting. The Nobel Symposia are very small meetings by invitation only and the number of key participants is usually in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. They have been made possible through a major grant from the Tri-Centennial Fund of the Bank of Sweden. Our first ideas to arrange a Nobel Symposium on many-body theory of atomic systems came up more than two years ago. It was quite obvious to us that a major break-through was happening in this field. Very accurate schemes have been available for some time for studying the static properties of small closed-shell atomic systems. By "atomic" systems we understand here atoms as well as free molecules, which can be treated by the same formalism, although the technical approaches might be quite different. The conceptual and computational developments in recent years, however, have made it possible to apply the many-body formalism also to heavier systems. Although no rigorous relativistic many-body theory yet exists, there seems to be a general agreement about the way relativistic calculations should be performed on normal atoms and molecules. Schemes based on relativistic perturbation theory as well as on relativistic multi- configurational Hartree-Fock are now in operation and a rapid development is expected in this area. Another field of atomic theory, where significant progress has been made recently, is in the application of many-body formalism to open-shell systems. General schemes, applicable to systems with one or several open shells, are now available, which will make it possible to apply many-body formalism to a much larger group of atomic systems and, in particular, to systems of more physical interest, A number of atomic properties - not only the correlation energy - can then be compared with the
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.
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.
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.
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
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.
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.
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.
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)
Ros, V.; Müller, M.; Scardicchio, A.
2015-11-01
We correct a small error in our article Integrals of motion in the many body localized phase[1]. The correction does not alter the main result regarding the convergence of the perturbative expansion for integrals of motion in forward approximation, but reduces the estimate of the radius of convergence by a numerical factor of roughly ≃1.79.
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
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.
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.
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
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)..
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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
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.
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
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.
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.
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
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
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
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.
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
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.
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.
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
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.
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
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.
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus
2015-05-01
Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.
NASA Astrophysics Data System (ADS)
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.
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.
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
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
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.
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.
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
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.
Order-disorder transitions in a sheared many-body system
NASA Astrophysics Data System (ADS)
Pfeifer, Jens C.; Bischoff, Tobias; Ehlers, Georg; Eckhardt, Bruno
2015-12-01
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped two-dimensional system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single-particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.
Description of pairing correlation in many-body finite systems with density functional theory
NASA Astrophysics Data System (ADS)
Hupin, Guillaume; Lacroix, Denis
2011-02-01
Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed earlier [D. Lacroix and G. Hupin, Phys. Rev. BPLRBAQ1098-012110.1103/PhysRevB.82.144509 82, 144509 (2010)] are carefully analyzed. Properties of quasiparticle states projected onto good particle numbers are first reviewed. These properties are used to (i) prove the existence of such a functional, (ii) provide an explicit functional through a 1/N expansion starting from the BCS approach, and (iii) give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picket-fence pairing Hamiltonian where even and odd systems are studied, using the blocking technique, at various particle numbers and coupling strengths, with uniform and random single-particle level spacing. In all cases, very good agreement is found, with a deviation of <1% compared to the exact energy.
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
Image method for Coulomb energy for many-body system of charged dielectric spheres
NASA Astrophysics Data System (ADS)
Qin, Jian; de Pablo, Juan; Freed, Karl
2015-03-01
Ion polarization is important for understanding ion solvation and the stability of ion clusters in polymeric materials which typically exhibit a low and spatially inhomogeneous dielectric permittivity. The simplest approach for modeling ion polarization involves treating the ions as charged spheres with an internal dielectric permittivity differing from that of the medium. The surface polarization contribution to the electrostatic energy for a system of such dielectric spheres can be evaluated perturbatively. We derived closed-form expressions for this energy as a function of the positions of an arbitrary number of polarized surfaces. Our approach is a generalization of the image method for conducting spheres. Using this approach, we calculated the polarization corrections to the cohesion energy for ion clusters and for densely packed ionic crystals. The method can be readily adapted for investigating ion polarization effects in both Monte Carlo and molecular dynamics simulations.
Influence of the interaction range on the thermostatistics of a classical many-body system
NASA Astrophysics Data System (ADS)
Cirto, Leonardo J. L.; Assis, Vladimir R. V.; Tsallis, Constantino
2014-01-01
We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/rα (α≥0). The approach is a first principle one (i.e., based on Newton’s law), and yields the probability distribution of momenta. For α large enough and N≫1 we observe, for longstanding states, the Maxwellian distribution, landmark of Boltzmann-Gibbs thermostatistics. But, for α small or comparable to unity, we observe instead robust fat-tailed distributions that are quite well fitted with q-Gaussians. These distributions extremize, under appropriate simple constraints, the nonadditive entropy Sq upon which nonextensive statistical mechanics is based. The whole scenario appears to be consistent with nonergodicity and with the thesis of the q-generalized Central Limit Theorem.
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.
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.
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.
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.
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.
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
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.
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
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.
NASA Astrophysics Data System (ADS)
Seki, K.; Yunoki, S.
2016-06-01
By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter η or the numerical extrapolation of η →0 . The method is conceptually based on the notion of the effective single-particle Hamiltonian which can be subtracted in the Lehmann representation of the single-particle Green's function within the CPT. Indeed, we show the general correspondence between the self-energy and the effective single-particle Hamiltonian which describes exactly the single-particle excitation energies of interacting fermions. The detailed formalism is provided for two-dimensional multiorbital systems and a benchmark calculation is performed for the two-dimensional single-band Hubbard model. The method can be adapted straightforwardly to symmetry-broken states, three-dimensional systems, and finite-temperature calculations.
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.
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.
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)
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.
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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].
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.
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)
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.
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
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.
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.
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.
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)
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
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.
On Many-Body Localization for Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-06-01
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
On Many-Body Localization for Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Imbrie, John Z.
2016-04-01
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
Many-body 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.
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.
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.
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.
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).
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.
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 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.
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.
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.
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.
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.
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.
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
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.
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
Goldfishing: A new solvable many-body problem
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-10-01
A recent technique allows one to identify and investigate solvable dynamical systems naturally interpretable as classical many-body problems, being characterized by equations of motion of Newtonian type (generally in two-dimensional space). In this paper we tersely review results previously obtained in this manner and present novel findings of this kind: mainly solvable variants of the goldfish many-body model, including models that feature isochronous classes of completely periodic solutions. Different formulations of these models are presented. The behavior of one of these isochronous dynamical systems in the neighborhood of its equilibrium configuration is investigated, and in this manner some remarkable Diophantine findings are obtained.
Non-equilibrium many body dynamics
Creutz, M.; Gyulassy, M.
1997-09-22
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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
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
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.
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).
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.
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 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.
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.
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.
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 .
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.
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.
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.
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 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.
Investigation of many-body forces in krypton and xenon
Salacuse, J.J.; Egelstaff, P.A.
1988-10-15
The simplicity of the state dependence at relatively high temperatures ofthe many-body potential contribution to the pressure and energy has been pointed out previously (J. Ram and P. A. Egelstaff, J. Phys. Chem. Liq. 14, 29 (1984); A. Teitsima and P. A. Egelstaff, Phys. Rev. A 21, 367 (1980)). In this paper, we investigate how far these many-body potential terms may be represented by simple models in the case of krypton on the 423-, 273-, 190-, and 150-K isotherms, and xenon on the 170-, 210-, and 270-K isotherms. At the higher temperatures the best agreement is found for the mean-field type of theory, and some consequences are pointed out. On the lower isotherms a state point is found where the many-body energy vanishes, and large departures from mean-field behavior are observed. This is attributed to the influence of short-ranged many-body forces.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Hermes, Matthew R.; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
NASA Astrophysics Data System (ADS)
Hermes, Matthew R.; Hirata, So
2014-08-01
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm-1 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
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.
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.
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
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.
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.