Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
arXiv:2110.04085 · doi:10.1103/PhysRevLett.128.180601
Abstract
The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal matrix elements are random numbers and the observables can be described by Random Matrix Theory (RMT). To what extent physical operators can be described by RMT, more precisely at which energy scale strict RMT description applies, is however not fully understood. We study this issue by introducing a novel numerical approach to probe correlations between matrix elements for Hilbert-space dimensions beyond those accessible for exact diagonalization. Our analysis is based on the evaluation of higher moments of operator submatrices, defined within energy windows of varying width. Considering nonintegrable quantum spin chains, we observe that genuine RMT behavior is absent even for narrow energy windows corresponding to time scales of the order of thermalization time of the respective observables. We also demonstrate that residual correlations between matrix elements are reflected in the dynamics of out-of-time-ordered correlation functions.
15 pages, 16 figures
References in corpus (10)
- Thermalization and its mechanism for generic isolated quantum systems
- Localization of interacting fermions at high temperature
- The Kernel Polynomial Method
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Chaos, Complexity, and Random Matrices
- Eigenstate thermalization within isolated spin-chain systems
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Equilibration time in many-body quantum systems
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