Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems

Abstract

We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum. In the quantum-chaotic model, we find that there is eigenstate thermalization; specifically, the matrix elements are Gaussian distributed with a variance that is a smooth function of $\omega =E_{\alpha }-E_{\beta }$ ({$E_{\alpha }$} are the eigenenergies) and scales as $1/D$ ($D$ is the Hilbert space dimension). In the interacting integrable model, we find that the matrix elements exhibit a skewed log-normal-like distribution and have a variance that is also a smooth function of $\omega$ that scales as $1/D$. We study in detail the low-frequency behavior of the variance of the matrix elements to unveil the regimes in which it exhibits diffusive or ballistic scaling. We show that in the quantum-chaotic model the behavior of the variance is qualitatively similar for matrix elements that connect eigenstates from the same versus different quasimomentum sectors. We also show that this is not the case in the interacting integrable model for observables whose translationally invariant counterpart does not break integrability if added as a perturbation to the Hamiltonian.

arXiv comment16 pages, 17 figures, as published

References in corpus (61)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• 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 thermalization through entanglement in an isolated many-body system
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Generalized Gibbs ensemble in integrable lattice models
• Experimental Observation of a Generalized Gibbs Ensemble
• The approach to thermal equilibrium in quantized chaotic systems
• Breakdown of thermalization in finite one-dimensional systems
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Finite-temperature transport in one-dimensional quantum lattice models
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• 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
• Hydrodynamic Diffusion in Integrable Systems
• Ultracold atoms out of equilibrium
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Finite-size scaling of eigenstate thermalization
• Quantum quenches and thermalization in one-dimensional fermionic systems
• Thermalization near integrability in a dipolar quantum Newton's cradle
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Super-diffusion in one-dimensional quantum lattice models
• Eigenstate thermalization within isolated spin-chain systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Thouless energy and multifractality across the many-body localization transition
• Eigenstate thermalization in the two-dimensional transverse field Ising model
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Entanglement and matrix elements of observables in interacting integrable systems
• Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
• 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
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Time-resolved observation of thermalization in an isolated quantum system
• Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
• Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
• Kardar-Parisi-Zhang universality from soft gauge modes
• 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
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• High-temperature coherent transport in the XXZ chain in the presence of an impurity
• Eigenstate thermalization hypothesis and integrals of motion
• Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
• Spin crossovers and superdiffusion in the one-dimensional Hubbard model
• Speck of Chaos
• Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
• Multipartite entanglement structure in the Eigenstate Thermalization Hypothesis
• Drude weight in systems with open boundary conditions
• Anomalous low-frequency conductivity in easy-plane XXZ spin chains
• Canonical Universality
• Persistent dark states in anisotropic central spin models
• Mechanism of slow equilibration of isolated quantum systems

Cited by in corpus (27)

• Universality in the onset of quantum chaos in many-body systems
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Classicality, Markovianity and local detailed balance from pure state dynamics
• Taking the temperature of a pure quantum state
• Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
• Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems
• Designs via Free Probability
• Tight-binding billiards
• Normal weak eigenstate thermalization
• Typicality of nonequilibrium (quasi-)steady currents
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Entropy and Temperature in finite isolated quantum systems
• Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
• Assigning Temperatures to Eigenstates
• Microcanonical Free Cumulants in lattice systems
• Quantum master equation from the eigenstate thermalization hypothesis
• Single-quasiparticle eigenstate thermalization
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Finite temperature single-particle Green's function in the Lieb-Liniger model
• Tunable Hilbert space fragmentation and extended critical regime
• Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems