Normal weak eigenstate thermalization
arXiv:2404.02199 · doi:10.1103/PhysRevB.110.104202
Abstract
Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak eigenstate thermalization has been proved to occur in general. Here, we unveil a stricter weak eigenstate thermalization phenomenon that occurs in quadratic models exhibiting quantum chaos in the single-particle sector (quantum-chaotic quadratic models) and in integrable interacting models. In such models, we argue that few-body observables that have a properly defined system-size independent norm are guaranteed to exhibit at least a polynomially vanishing variance (over the entire many-body energy spectrum) of the diagonal matrix elements, a phenomenon we dub normal weak eigenstate thermalization. We prove that normal weak eigenstate thermalization is a consequence of single-particle eigenstate thermalization, i.e., it can be viewed as a manifestation of quantum chaos at the single-particle level. We report numerical evidence of normal weak eigenstate thermalization for quantum-chaotic quadratic models such as the three-dimensional Anderson model in the delocalized regime and the power-law random banded matrix model, as well as for the integrable interacting spin-1/2 XYZ and XXZ models.
20 pages, 12 figures, as published
References in corpus (96)
- Thermalization and its mechanism for generic isolated quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Quantum many-body systems out of equilibrium
- Quantum Quench in the Transverse Field Ising Chain
- Generalized Gibbs ensemble in integrable lattice models
- Quantum mechanical evolution towards thermal equilibrium
- Eigenstate Thermalization Hypothesis
- Time evolution of local observables after quenching to an integrable model
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Breakdown of thermalization in finite one-dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- The Luttinger model following a sudden interaction switch-on
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Complete Generalized Gibbs Ensemble in an interacting Theory
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Generalized Thermalization in an Integrable Lattice System
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Quantum quench dynamics of the Luttinger model
- Quantum quench dynamics of some exactly solvable models in one dimension
- Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
- Finite-size scaling of eigenstate thermalization
- Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
- Quantum quenches and thermalization in one-dimensional fermionic systems
- Quantum Many-Body Scars: A Quasiparticle Perspective
- Quantum equilibration in finite time
- Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
- Equilibration of quantum systems and subsystems
- Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
- Dynamical Correlations after a Quantum Quench
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Eigenstate thermalization within isolated spin-chain systems
- Statistical localization: from strong fragmentation to strong edge modes
- Can we study the many-body localisation transition?
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- Thouless energy and multifractality across the many-body localization transition
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- Entanglement and matrix elements of observables in interacting integrable systems
- Bounds on chaos from the eigenstate thermalization hypothesis
- Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
- Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
- Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
- Eigenstate Thermalization in a Locally Perturbed Integrable System
- Long tail distributions near the many body localization transition
- Equilibration of isolated macroscopic quantum systems
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
- Fluctuation Theorem for Many-Body Pure Quantum States
- Return probability for the Anderson model on the random regular graph
- Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
- Eigenstate Thermalization Hypothesis and Free Probability
- Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
- Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
- Eigenstate Thermalization, Random Matrix Theory and Behemoths
- Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
- Eigenstate Correlations, Thermalization and the Butterfly Effect
- Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
- Equilibration via Gaussification in fermionic lattice systems
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Eigenstate thermalization hypothesis and integrals of motion
- Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
- Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
- Speck of Chaos
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Single-particle and many-body analyses of a quasiperiodic integrable system after a quench
- Eigenstate thermalization hypothesis through the lens of autocorrelation functions
- Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
- Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
- Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
- Relaxation Dynamics of Disordered Spin Chains: Localization and the Existence of a Stationary State
- Critical Exponent of the Anderson Transition using Massively Parallel Supercomputing
- Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models
- Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
- Gaussian Equilibration
- Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization
- Equilibration towards generalized Gibbs ensembles in non-interacting theories
- Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
- Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians
- Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
- Statistics of correlation functions in the random Heisenberg chain
- Eigenstate Thermalization in Long-Range Interacting Systems
- Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
- Dynamical typicality approach to eigenstate thermalization
- Scale-invariant critical dynamics at eigenstate transitions
- Generalized thermalization in quantum-chaotic quadratic Hamiltonians
- Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
- Equilibration of isolated many-body quantum systems with respect to general distinguishability measures
- Eigenstate entanglement entropy in the integrable spin- XYZ model
- Single-quasiparticle eigenstate thermalization
- Eigenstate Thermalisation on Average
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- Many-Body Localization in the Age of Classical Computing
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- Open-system eigenstate thermalization in a noninteracting integrable model
- Integrability versus chaos in the steady state of many-body open quantum systems
- Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath
- Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
- Ensemble-averaged mean-field many-body level density: an indicator of integrable versus chaotic single-particle dynamics
- Thermalization is typical in large classical and quantum harmonic systems
- Quadratic Hamiltonian approach to heat transport in fermionic systems
- Localization transitions in quadratic systems without quantum chaos
- Tunable Hilbert space fragmentation and extended critical regime