Eigenstate thermalization hypothesis and integrals of motion

Abstract

Even though foundations of the eigenstate thermalization hypothesis (ETH) are based on random matrix theory, physical Hamiltonians and observables substantially differ from random operators. One of the major challenges is to embed local integrals of motion (LIOMs) within the ETH. Here we focus on their impact on fluctuations and structure of the diagonal matrix elements of local observables. We first show that nonvanishing fluctuations entail the presence of LIOMs. Then we introduce a generic protocol to construct observables, subtracted by their projections on LIOMs as well as products of LIOMs. The protocol systematically reduces fluctuations and/or the structure of the diagonal matrix elements. We verify our arguments by numerical results for integrable and nonintegrable models.

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Cited by in corpus (43)

• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Statistical localization: from strong fragmentation to strong edge modes
• Many-Body Localization in the Age of Classical Computing
• Eigenstate Thermalization in a Locally Perturbed Integrable System
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Entanglement spreading in non-equilibrium integrable systems
• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• 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
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
• Phenomenology of spectral functions in disordered spin chains at infinite temperature
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Eigenstate Thermalization in Long-Range Interacting Systems
• Signatures of a critical point in the many-body localization transition
• Revisiting the Mazur bound and the Suzuki equality
• Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
• Hydrodynamics and the eigenstate thermalization hypothesis
• Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems
• Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
• Tight-binding billiards
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Normal weak eigenstate thermalization
• All Local Conserved Quantities of the One-Dimensional Hubbard Model
• Eigenstate thermalization scaling in approaching the classical limit
• Entropy and Temperature in finite isolated quantum systems
• Assigning Temperatures to Eigenstates
• Finite-size scaling analysis of eigenstate thermalization
• Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems
• Local integrals of motion in dipole-conserving models with Hilbert space fragmentation
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Single-quasiparticle eigenstate thermalization
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks
• Integrability versus chaos in the steady state of many-body open quantum systems
• Finite-size scaling analysis of localization transitions in the disordered two-dimensional Bose-Hubbard model within the fluctuation operator expansion method
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• Tunable Hilbert space fragmentation and extended critical regime
• Temperature and conditions for thermalization after canonical quenches