Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Y35: Thermalization and Many-Body Localization |
Hide Abstracts |
Sponsoring Units: DAMOP Chair: Andrew Daley, University of Pittsburgh Room: 702 |
Friday, March 7, 2014 8:00AM - 8:12AM |
Y35.00001: Role of the Initial State in the Nonequilibrium Quantum Dynamics of Many-Body Systems Lea F. Santos, Eduardo J. Torres-Herrera We show that the dynamics of isolated many-body quantum systems after a quench depends on the interplay between the initial state and the Hamiltonian dictating the evolution. The systems considered are in the nonperturbative regime. The relaxation process is controlled by the width of the energy distribution of the initial state and may be very similar for both chaotic and integrable Hamiltonians. Our analytical expression for the fidelity decay displays excellent agreement with our numerical results. This decay is Gaussian and may persist until saturation. We also provide analytical expressions that describe very well the initial evolution of the Shannon entropy and of few-body observables. The analyses are developed for deterministic one-dimensional systems and initial states of interest to current experiments with cold atoms in optical lattices. [Preview Abstract] |
Friday, March 7, 2014 8:12AM - 8:24AM |
Y35.00002: On thermalization in a nonintegrable quantum system: who thermalizes? Hyungwon Kim, Mari Carmen Banuls, David Huse, Ignacio Cirac We study properties of local operators with a nonintegrable Hamiltonian. We look for the cases where non-thermal (nonequilibrium) behaviors may be persistent even in the long time limit. First, we consider eigenstates which do not obey the Eigenstate Thermalization Hypothesis (ETH) in a finite size system. We show that the expectation values of local observable of these ``outliers'' converge to the scenario of ETH as we increase the system size. Next, we construct a local operator that gives the smallest value of commutator with the Hamiltonian. As we increase the range of the operator, the commutator quickly decreases with the range. This may imply the existence of local operators which may take fairly long to thermalize. [Preview Abstract] |
Friday, March 7, 2014 8:24AM - 8:36AM |
Y35.00003: Finite-size scaling of eigenstate thermalization Wouter Beugeling, Roderich Moessner, Masud Haque According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Since isolated systems are by nature finite, the finite-size scaling of such fluctuations is a central aspect of the ETH. We propose that for generic non-integrable systems these fluctuations scale with a universal power law in the dimension of the Hilbert space. We present extensive multiple-system numerical evidence for this scaling law and provide supporting arguments. We also show how the scaling changes when approaching integrability. [Preview Abstract] |
Friday, March 7, 2014 8:36AM - 8:48AM |
Y35.00004: Relaxation towards negative absolute temperature states Stephan Mandt, Adrian Feiguin, Salvatore Manmana Motivated by the recent experimental observation of negative absolute temperature states with ultracold atoms in optical lattices, [Braun et al., Science 339 52 (2013)], we discuss the formation of these states. More specifically, we consider the relaxation after a sudden inversion of the external parabolic confining potential. First, previous numerical simulation results of a semiclassical Boltzmann equation for the case of fermions will be discussed, which show a surprisingly slow equilibration due to the diffusive rearrangement of the local kinetic energies in the inhomogeneous system. We then focus on the integrable system of one-dimensional hard-core bosons. Here, we provide convincing numerical evidence for the relaxation to a generalized Gibbs ensemble at negative absolute temperature, a notion we define in this context. [Preview Abstract] |
Friday, March 7, 2014 8:48AM - 9:00AM |
Y35.00005: Thermalization timescales in a 1d Hubbard model with slightly broken integrability Fabian Biebl, Stefan Kehrein Understanding relaxation in quantum systems is essential to determine whether an experimental setup can be described by equilibrium concepts. For example integrable systems do not thermalize, but develop into non-thermal steady states. By slightly breaking integrability, thermalization of such non-thermal (prethermalized) states becomes possible. An important question is to identify the corresponding timescale for thermalization due to the breaking of integrability. We investigate this question for a fermionic Hubbard chain. The integrability breaking term is a small next to nearest neighbor hopping term [1,2]. The thermalization timescale is extracted from the quantum Boltzmann equation and depends strongly on temperature.\\[4pt] [1] M. L. R. F\"urst et al., Phys. Rev. E 86, 031122 (2012).\\[0pt] [2] M. L. R. F\"urst et al., Phys. Rev. E 88, 012108 (2013). [Preview Abstract] |
Friday, March 7, 2014 9:00AM - 9:12AM |
Y35.00006: Relaxation and thermalization of isolated quantum many-body systems after a local quench Eduardo J. Torres-Herrera, Lea F. Santos A single on-site defect in the middle of a one-dimensional spin-1/2 XXZ model is enough to break its integrability. By quenching the excess energy of the defect, we investigate the relaxation process for various initial states and the viability of thermalization. Changing the defect energy is equivalent to weakly perturbing the system, which prevents the initial state (projected into the energy eigenbasis) from achieving a Gaussian shape; it has instead a Breit-Wigner form. We show that in this scenario, the relaxation process is slower and the role of the Eigenstate Thermalization Hypothesis becomes more prominent. [Preview Abstract] |
Friday, March 7, 2014 9:12AM - 9:24AM |
Y35.00007: Exact analysis of prethermalization of a coherently split one-dimensional Bose gas Eriko Kaminishi, Tatsuhiko Ikeda, Takashi Mori, Masahito Ueda We theoretically study the prethermalization dynamics of a coherently split one-dimensional Bose gas by using the Bethe ansatz method. Prethermalization is a relaxation process to a quasi-stationary state before reaching the true equilibrium state. The concept of prethermalization is important for understanding the fundamental aspects of quantum statistical mechanics such as ``equilibration'' and ``relaxation'' in isolated quantum many-body systems. Prethermalization and its connection to integrability in one-dimensional quantum systems have been intensively studied by both experiments and theories. For instance, M. Gring et al. recently observed the evolution of a rapidly and coherently split one-dimensional Bose gas for large numbers of particles and compare the evolution of the system to the prediction of the Tomonaga-Luttinger liquid (TLL) theory. Here we employ the Bethe ansatz method and precisely analyze the prethermalization process over a long-time scale beyond the TLL prediction. [Preview Abstract] |
Friday, March 7, 2014 9:24AM - 9:36AM |
Y35.00008: Random matrix study of the time scale of thermalization after a quantum quench Tatsuhiko Ikeda, Yu Watanabe Thermalization in isolated quantum systems has been theoretically predicted and actually observed in experiments by using, for example, the cold atoms. However, the time scale, which the theories of thermalization require as a sufficient condition, is exponentially large in the number of particles and thus too large compared with that observed in experiments. We study thermalization after a quantum quench which is described by random matrices, in particular the sparse Gaussian Unitary Ensemble, and show that the time scale is given by $\tau_{\rm eq} =\hbar/[2\sigma(H)]$, where $\sigma(H)$ is the energy fluctuation of the initial state. Since the energy fluctuation grows only polynomially in the number of particles, this time scale can be regarded as more realistic one than the sufficient condition mentioned above. We also conduct numerical simulations of quantum quenches in the hard-core Bose-Hubbard model to validate the result in physically realistic situations. [Preview Abstract] |
Friday, March 7, 2014 9:36AM - 9:48AM |
Y35.00009: Equilibration and Generalized GGE in Tonks Girardeau Regime Garry Goldstein, Natan Andrei We study the nonequilibrium properties of the 1-D Lieb-Liniger model in the infinite repulsion Tonks-Girardeau regime, Introducing a new version of the Yudson representation applicable to finite sized systems and appropriately taking the infinite volume limit we are able to study the equilibration of the Lieb-Liniger gas in the thermodynamic limit. We provide a formalism to compute various correlation functions for highly non-equilibrium initial states. In the Tonks Girardeua limit we are able to find explicit analytic expressions for the long time limit of the expectation of the density, density density and related correlation functions. We show that the gas equilibrates to a steady state from arbitrary initial states with ``smooth'' correlation functions. For nearly translationally invariant states the gas equilibrates to a diagonal ensemble which we show is equivalent to a generalized version of the GGE for sufficiently simple correlation functions, which in particular include density density correlations. [Preview Abstract] |
Friday, March 7, 2014 9:48AM - 10:00AM |
Y35.00010: Characterizing a conducting-to-nonconducting transition in an inhomogeneous Hubbard model out of equilibrium via tDMRG simulations Daniel Gruss, Chih-Chun Chien, Massimiliano Di Ventra, Michael Zwolak The study of time-dependent, many-body transport phenomena is increasingly within reach of ultra-cold atom experiments. These systems not only allow experimental emulation of solid state systems, but allow us to probe the dynamics of transport at a previously unreachable level of detail. We will discuss computational results for the dynamics of fermionic transport in optical lattices that emulate an inhomogeneous Hubbard model. We demonstrate that this system displays a many-body, nonequilibrium conducting to nonconducting transition that depends on the interaction strength and filling.\footnote{New J. Phys. 15 063026} We characterize the transition by deconstructing the dynamical behavior of the fermionic density. We will also discuss these results in the context of present-day cold atom experiments. [Preview Abstract] |
Friday, March 7, 2014 10:00AM - 10:12AM |
Y35.00011: Non-equilibrium dynamics and state preparation in bilayer optical lattices Stephan Langer, Andrew J. Daley We study dynamical schemes to obtain low entropy ground states of strongly interacting many body systems. The focus of our work is on ultra-cold Bose and Fermi gases in bilayer optical lattice systems with separately tunable interlayer coupling, energy offset between the layers and repulsive interactions. The case of two coupled one-dimensional chains is treated in a numerically exact manner using the adaptive time-dependent density matrix renormalization group which allows us to study the change of offset and interlayer coupling in real time. We identify parameter regimes where the ground state of the coupled system in the limit of small interlayer coupling consists of a Mott insulator in one layer and a superfluid/metallic state in the other layer can serve as an entropy reservoir. We then investigate the time-dependent dynamics of this system, studying entropy transfer between layers and the emergence of characteristic many-body correlations as we change the layer offset energy and coupling strength. In addition to applications as a preparation scheme for fully interacting Mott-insulator states, feasible with available experimental techniques, the investigated protocols could be easily adapted to also allow for a controlled preparation of highly excited states. [Preview Abstract] |
Friday, March 7, 2014 10:12AM - 10:24AM |
Y35.00012: Nonequilibrium Dynamics beyond the Mean Field Approximation Ingo Homrighausen, Stefan Kehrein Mean field type approximations are one of the most accessible methods to study the complexity of quantum many body systems out of equilibrium. However, the validity of such approximations has to be examined in each case. Building on Ref. [1] we investigate three different quantum many particle models on finite fully connected lattices: the transverse field Ising model, the Bose-Hubbard model and the Jaynes Cummings model. In particular, we explore the nonequilibrium dynamics of the order parameter and its variance after a quantum quench. The most intriguing observation is that all three models exhibit the same universal behavior: For quenches within the ordered phase, the variance of the order parameter shows a quasiperiodic breathing behavior. The local maxima of this breathing increase in time whereas the local minima decrease. Applying a semiclassical expansion, we explain these findings and argue why the observations are generic. We also discuss the time scale of validity of our analysis by comparing to numerically exact data. [1] B. Sciolla, G. Biroli, J. Stat. Mech. (2011) P11003. [Preview Abstract] |
Friday, March 7, 2014 10:24AM - 10:36AM |
Y35.00013: Dynamical quantum phase transitions in random spin chains Ronen Vosk, Ehud Altman Quantum systems can exhibit a great deal of universality at low temperature due to the structure of ground states and the critical points separating distinct states. On the other hand, quantum time evolution of the same systems involves all energies and it is therefore thought to be much harder, if at all possible, to have sharp transitions in the dynamics. In this paper we show that phase transitions characterized by universal singularities do occur in the time evolution of random spin chains. The sharpness of the transitions and integrity of the phases owes to many-body localization, which prevents thermalization in these systems. Using a renormalization group approach, we solve the time evolution of random Ising spin chains with generic interactions starting from initial states of arbitrary energy. As a function of the Hamiltonian parameters, the system is tuned through a dynamical transition, similar to the ground state critical point, at which the local spin correlations establish true long range temporal order. As in ground state quantum phase transitions, the dynamical transition has unique signatures in the entanglemenent properties of the system. [Preview Abstract] |
Friday, March 7, 2014 10:36AM - 10:48AM |
Y35.00014: Entanglement properties after a partial measurement: a numerical study of excited states in Hubbard-like models James R. Garrison, Ryan V. Mishmash, Tarun Grover, Matthew P.A. Fisher Our growing understanding of entanglement in condensed matter systems continues to provide incredible insight into characterizing phases of matter. Recently, progress in many-body localization (MBL) has revealed a deep connection between the entanglement properties of finite energy density eigenstates and whether or not the state is thermalized. Inspired by developments in MBL as well as a desire to identify and characterize a proposed ``quantum disentangled liquid,'' we have performed exact diagonalization studies on one-dimensional Hubbard-like models. Specifically, we begin with an excited energy eigenstate, perform a partial measurement (e.g., measure the total spin on each site), and study the properties of the resulting wave function. By numerically studying small systems, we can gain insights into whether spin and charge thermalize independently, and develop intuition which may one day guide experiments on cold atom systems. [Preview Abstract] |
Friday, March 7, 2014 10:48AM - 11:00AM |
Y35.00015: Many-body Localization with Dipoles Norman Yao, Chris Laumann, Sarang Gopalakrishnan, Michael Knap, Markus Mueller, Eugene Demler, Mikhail Lukin Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration; when equilibration fails, so does much of our understanding. In isolated quantum systems, this breakdown is captured by the phenomenon known as many-body localization. I will briefly introduce the basic phenomena of many-body localization and review its theoretical status. To date, none of these phenomena has been observed in an experimental system, in part because of the isolation required to avoid thermalization. I will consider several dipolar systems which we believe to be ideal platforms for the realization of MBL phases and for investigating the associated delocalization phase transition. The power law of the dipolar interaction immediately raises the question: can localization in real space persist in the presence of such long-range interactions? I will review and extend several arguments producing criteria for localization in the presence of power laws and present small-scale numerics regarding the MBL transition in several of the proposed dipolar systems. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2021 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700