Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis

Abstract

A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have thermal properties. We numerically investigate the ETH by focusing on the large deviation property, which directly evaluates the ratio of athermal energy eigenstates in the energy shell. As a consequence, we have systematically confirmed that the strong ETH is indeed true even for near-integrable systems, where we found that the finite-size scaling of the ratio of athermal eigenstates is double exponential. Our result illuminates universal behavior of quantum chaos, and suggests that large deviation analysis would serve as a powerful method to investigate thermalization in the presence of the large finite-size effect.

References in corpus (43)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• The large deviation approach to statistical mechanics
• 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 thermalization through entanglement in an isolated many-body system
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
• Strongly correlated fermions after a quantum quench
• Ergodic dynamics and thermalization in an isolated quantum system
• Finite-size scaling of eigenstate thermalization
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Eigenstate thermalization within isolated spin-chain systems
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Subsystem ETH
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Quantum chaos and thermalization in gapped systems
• Eigenstate thermalization in the two-dimensional transverse field Ising model
• Emergence of quasi-condensates of hard-core bosons at finite momentum
• Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
• Fluctuation Theorem for Many-Body Pure Quantum States
• Crossover from Poisson to Wigner-Dyson Level Statistics in Spin Chains with Integrability Breaking
• Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
• Exactly conserved quasilocal operators for the XXZ spin chain
• Generalization of von Neumann's Approach to Thermalization
• Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
• Relevance of the eigenstate thermalization hypothesis for thermal relaxation
• Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?
• Numerical construction of a low-energy effective Hamiltonian in a self-consistent Bogoliubov-de Gennes approach of superconductivity

Cited by in corpus (51)

• Entanglement and matrix elements of observables in interacting integrable systems
• Eigenstate Thermalization in a Locally Perturbed Integrable System
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Eigenstate Thermalization, Random Matrix Theory and Behemoths
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field
• Bounds in Nonequilibrium Quantum Dynamics
• Thermalization and Heating Dynamics in Open Generic Many-Body Systems
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
• Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Eigenstate entanglement: Crossover from the ground state to volume laws
• Dynamical typicality approach to eigenstate thermalization
• Quantum Chaotic Fluctuation-Dissipation Theorem: Effective Brownian Motion in Closed Quantum Systems
• Guide to Exact Diagonalization Study of Quantum Thermalization
• Statistical mechanics for non-Hermitian quantum systems
• Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
• Eigenstate entanglement scaling for critical interacting spin chains
• Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
• Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
• Tight-binding billiards
• Work Extraction from a Single Energy Eigenstate
• Normal weak eigenstate thermalization
• Typicality of nonequilibrium (quasi-)steady currents
• Refining Deutsch's approach to thermalization
• Continuous-time quantum walks for MAX-CUT are hot
• Entropy and Temperature in finite isolated quantum systems
• Eigenstate thermalization scaling in approaching the classical limit
• Thermalization of locally perturbed many-body quantum systems
• Assigning Temperatures to Eigenstates
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Eigenstate Fluctuation Theorem in the Short and Long Time Regimes
• Deep reinforcement learning for preparation of thermal and prethermal quantum states
• Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
• Heating and Cooling of Quantum Gas by Eigenstate Joule Expansion
• Scaling functions for eigenstate entanglement crossovers in harmonic lattices
• Single-quasiparticle eigenstate thermalization
• Eigenstate Thermalisation on Average
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Continuous-time quantum optimisation without the adiabatic principle
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• The second law of thermodynamics from concavity of energy eigenvalues
• Quantum Joule Expansion of One-Dimensional Systems
• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
• Kinetically constrained models constructed from dissipative quantum dynamics
• The second law of thermodynamics from concave energy in classical mechanics
• Nonergodic delocalized paramagnetic states in quantum neural networks
• Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit