Eigenstate Thermalization, Random Matrix Theory and Behemoths

Abstract

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this paper. We report on the construction of highly nonlocal operators, Behemoths, that are building blocks for various kinds of local and non-local operators. The Behemoths have a singular distribution and width $w\sim {\mathcal{D}}^{-1}$ ($\mathcal{D}$ being the Hilbert space dimension). From them, one may construct local operators with the ordinary Gaussian distribution and $w\sim {\mathcal{D}}^{-1/2}$ in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with $w\sim {\mathcal{D}}^{-\delta }$, $0<\delta <1/2$. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of non-integrable many-body systems.

12 pages (5 in main text), 8 figures (4 in main text)

References in corpus (22)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization: an introduction and selected topics
• Eigenstate Thermalization Hypothesis
• Breakdown of thermalization in finite one-dimensional systems
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Ergodicity breaking in a model showing many-body localization
• Anomalous thermalization in ergodic systems
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Eigenstate thermalization within isolated spin-chain systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Quantum chaos and thermalization in gapped systems
• Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
• Statistical properties of eigenstate amplitudes in complex quantum systems
• Relaxation and Thermalization after a Quantum Quench: Why Localization is Important
• The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
• Dynamical typicality approach to eigenstate thermalization

Cited by in corpus (56)

• Entanglement and matrix elements of observables in interacting integrable systems
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Chaos and ergodicity across the energy spectrum of interacting bosons
• Multifractality meets entanglement: relation for non-ergodic extended states
• Eigenstate thermalization hypothesis and integrals of motion
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Speck of Chaos
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Localization transition on the Random Regular Graph as an unstable tricritical point in a log-normal Rosenzweig-Porter random matrix ensemble
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Bounds in Nonequilibrium Quantum Dynamics
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Interacting bosons in a triple well: Preface of many-body quantum chaos
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Statistics of correlation functions in the random Heisenberg chain
• Classicality, Markovianity and local detailed balance from pure state dynamics
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Chaos and Thermalization in the Spin-Boson Dicke Model
• Anisotropy-mediated reentrant localization
• Chaos in the Bose-Hubbard model and random two-body Hamiltonians
• Power-law entanglement growth from typical product states
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Tight-binding billiards
• Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems
• Normal weak eigenstate thermalization
• Probability transport on the Fock space of a disordered quantum spin chain
• Quantum Chaos in the Extended Dicke Model
• Eigenstate thermalization scaling in approaching the classical limit
• Entropy and Temperature in finite isolated 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
• The ergodic and non-ergodic phases in one dimensional clean Jaynes-Cummings-Hubbard system
• Quantum master equation from the eigenstate thermalization hypothesis
• Single-quasiparticle eigenstate thermalization
• Ground state-based quantum feature maps
• Nontrivial damping of quantum many-body dynamics
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model
• Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems
• Chaos enhancement in large-spin chains
• Integrability versus chaos in the steady state of many-body open quantum systems
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Out-of-equilibrium Eigenstate Thermalization Hypothesis
• Does the Eigenstate Thermalization Hypothesis Imply Thermalization?
• Equilibration and the eigenstate thermalization hypothesis as limits to observing macroscopic quantum superpositions
• Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems