Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables

Abstract

We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a function of the eigenstate energy differences, and show that it is in accordance with the eigenstate thermalization hypothesis ansatz.

10 pages, 9 figures, as published

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum Quench in the Transverse Field Ising Chain
• Experimental Observation of a Generalized Gibbs Ensemble
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• Dynamical phase transition in correlated fermionic lattice systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Strong and weak thermalization of infinite non-integrable quantum systems
• Strongly correlated fermions after a quantum quench
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Anomalous thermalization in ergodic systems
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Eigenstate thermalization within isolated spin-chain systems
• Quantum chaos and thermalization in gapped systems
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
• Quenches in a quasi-disordered integrable lattice system: Dynamics and statistical description of observables after relaxation
• Relevance of the eigenstate thermalization hypothesis for thermal relaxation
• Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize

Cited by in corpus (102)

• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Quantum chaos challenges many-body localization
• Non-Hermitian Many-Body Localization
• Nonthermal states arising from confinement in one and two dimensions
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Entanglement and matrix elements of observables in interacting integrable systems
• Many-Body Localization in the Age of Classical Computing
• Universality classes of non-Hermitian random matrices
• Eigenstate Thermalization in a Locally Perturbed Integrable System
• Signatures of rare states and thermalization in a theory with confinement
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Onset of Floquet Thermalisation
• Universality in the onset of quantum chaos in many-body systems
• Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
• Eigenstate Thermalization, Random Matrix Theory and Behemoths
• Probing thermality beyond the diagonal
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• ETH and Modular Invariance of 2D CFTs
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Eigenstate thermalization hypothesis and integrals of motion
• A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Time evolution of correlation functions in quantum many-body systems
• Bound on Eigenstate Thermalization from Transport
• Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation
• Many-body scar state intrinsic to periodically driven system: Rigorous results
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Multipartite entanglement structure in the Eigenstate Thermalization Hypothesis
• Extremal Correlators and Random Matrix Theory
• Statistical properties of eigenstate amplitudes in complex quantum systems
• 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
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization
• Hilbert space shattering and dynamical freezing in the quantum Ising model
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Eigenstate thermalization hypothesis in quantum dimer models
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Atypicality of Most Few-Body Observables
• Eigenstate thermalization and rotational invariance in ergodic quantum systems
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"
• Canonical Universality
• Anomalous thermalization and transport in disordered interacting Floquet systems
• Eigenstate Thermalization in Long-Range Interacting Systems
• Spectral decoupling in many-body quantum chaos
• Quantum Chaotic Fluctuation-Dissipation Theorem: Effective Brownian Motion in Closed Quantum Systems
• Eigenstate thermalization from the clustering property of correlation
• Degenerate observables and the many Eigenstate Thermalization Hypotheses
• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
• Taking the temperature of a pure quantum state
• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Exponential damping induced by random and realistic perturbations
• Quantum thermalization and Virasoro symmetry
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
• Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
• Classical algorithms for many-body quantum systems at finite energies
• Tight-binding billiards
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems
• Normal weak eigenstate thermalization
• Universality classes of thermalization for mesoscopic Floquet systems
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Generalized Free Cumulants for Quantum Chaotic Systems
• Modern Concepts of Quantum Equilibration Do Not Rule Out Strange Relaxation Dynamics
• Entropy and Temperature in finite isolated quantum systems
• Continuous-time quantum walks for MAX-CUT are hot
• Eigenstate thermalization scaling in approaching the classical limit
• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
• Assigning Temperatures to Eigenstates
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• From integrability to chaos: the quantum-classical correspondence in a triple well bosonic model
• Eigenstate Fluctuation Theorem in the Short and Long Time Regimes
• Quantum eigenstates from classical Gibbs distributions
• Stability of Quantum Dynamics under Constant Hamiltonian Perturbations
• Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Single-quasiparticle eigenstate thermalization
• Decoherence Entails Exponential Forgetting in Systems Complying with the Eigenstate Thermalization Hypothesis
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Prethermalization of light and matter in cavity-coupled Rydberg arrays
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Remarks on effects of projective phase on eigenstate thermalization hypothesis
• Continuous-time quantum optimisation without the adiabatic principle
• Key Observable for Linear Thermalization
• Quantum Joule Expansion of One-Dimensional Systems
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Out-of-equilibrium Eigenstate Thermalization Hypothesis
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Product of Random States and Spatial (Half-)Wormholes
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• A Heuristic for Matrix Product State Simulation of Out-of-Equilibrium Dynamics of Two-Dimensional Quantum Spin Systems
• Density matrix of chaotic quantum systems
• Volume-law entanglement entropy of typical pure quantum states