Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems
arXiv:1906.11856 · doi:10.1103/PhysRevB.101.174312
Abstract
Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.
arXiv comment18 pages, 7 figures (as published)
References in corpus (58)
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- The many-body localization phase transition
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Non-local propagation of correlations in long-range interacting quantum systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Spin-Glass Theory for Pedestrians
- Quantum chaos challenges many-body localization
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- The Ergodic Side of the Many-Body Localization Transition
- Out-of-Time-Order Correlation for Many-Body Localization
- Solution of a minimal model for many-body quantum chaos
- Chaos, Complexity, and Random Matrices
- Quantum equilibration in finite time
- Equilibration of quantum systems and subsystems
- Dynamics at the Many-Body Localization Transition
- Thouless energy and multifractality across the many-body localization transition
- Spectral statistics and many-body quantum chaos with conserved charge
- Thouless and relaxation time scales in many-body quantum systems
- Typical fast thermalization processes in closed many-body systems
- Lack of Self-Averaging in Critical Disordered Systems
- Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach
- The spectral form factor is not self-averaging
- Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
- Return probability for the Anderson model on the random regular graph
- Entanglement versus chaos in disordered spin chains
- Structure of eigenstates and quench dynamics at an excited state quantum phase transition
- Quench Dynamics of Isolated Many-Body Quantum Systems
- Time Fluctuations in Isolated Quantum Systems of Interacting Particles
- General Features of the Relaxation Dynamics of Interacting Quantum Systems
- Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
- Dynamical Manifestations of Quantum Chaos: Correlation Hole and Bulge
- Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model
- Unconventional decay law for excited states in closed many-body systems
- Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization
- On the Area Law for Disordered Free Fermions
- Power-law decay exponents: a dynamical criterion for predicting thermalization
- Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
- Realistic many-body quantum systems vs full random matrices: static and dynamical properties
- Interplay between interaction and (un)correlated disorder in one-dimensional many-particle systems: delocalization and global entanglement
- Relaxation and Thermalization of Isolated Many-Body Quantum Systems
- Exact Quantum Decay of an Interacting Many-Particle System: the Calogero-Sutherland model
- Structure of wavefunctions in (1+2)-body random matrix ensembles
- Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization
- Universal Fluctuations of Single-Particle Diffusivity in Quenched Environment
- Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
- Exponentially fast dynamics of chaotic many-body systems
- Semiclassical form factor of matrix element fluctuations
- Analytical description of the survival probability of coherent states in regular regimes
- Non-self-averaging behaviors and ergodicity in quenched trap model with finite system size
- Random walks and polymers in the presence of quenched disorder
- Is small-world network disordered?
- Transportless equilibration in isolated many-body quantum systems
- Floquet topological transition by unpolarized light
- Self-averaging characteristics of spectral fluctuations
- Self--averaging of random quantum dynamics
- Does Quantum Chaos Explain Quantum Statistical Mechanics?
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- Interacting bosons in a triple well: Preface of many-body quantum chaos
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- Self-averaging in many-body quantum systems out of equilibrium. II. Approach to the localized phase
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- Catching thermal avalanches in the disordered XXZ model
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- Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions
- Many-Body Mobility Edge in Quantum Sun models
- Equilibration on average in quantum processes with finite temporal resolution
- Ergodicity probes: using time-fluctuations to measure the Hilbert space dimension
- Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
- Universal equilibration dynamics of the Sachdev-Ye-Kitaev model
- Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields
- Many-body localization crossover is sharper in quasiperiodic spin chains
- Decomposing the Spectral Form Factor
- Effects of auto-correlated disorder on the dynamics in the vicinity of the many-body localization transition
- Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
- Integrability breaking and bound states in Google's decorated XXZ circuits
- Random matrix universality in dynamical correlation functions at late times
- Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands
- Transport and integrability-breaking in non-Hermitian many-body quantum systems
- Engineering complete delocalization of single particle states in a class of one dimensional aperiodic lattices: a quantum dynamical study
- Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
- Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity
- Hierarchy of timescales in a disordered spin- XX ladder
- Late-time universal distribution functions of observables in one-dimensional many-body quantum systems
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