Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time

Jiaozi Wang, Mats H. Lamann, Jonas Richter, Robin Steinigeweg, Anatoly Dymarsky, Jochen Gemmer

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16 Scopus citations


The eigenstate thermalization hypothesis explains the emergence of the thermodynamic equilibrium in isolated quantum many-body systems by assuming a particular structure of the 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 a RMT description applies, more precisely at which energy scale matrix elements of physical operators become truly uncorrelated, 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 by 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 matrix elements remain correlated even for narrow energy windows corresponding to timescales of the order of thermalization time of the respective observables. We also demonstrate that such residual correlations between matrix elements are reflected in the dynamics of out-of-time-ordered correlation functions.

Original languageEnglish
Article number180601
JournalPhysical Review Letters
Issue number18
StatePublished - May 6 2022

Bibliographical note

Funding Information:
This work has been funded by the Deutsche Forschungsgemeinschaft (DFG), Grants No. 397107022 (GE 1657/3-2), No. 397067869 (STE 2243/3-2), and No. 355031190, within the DFG Research Unit FOR 2692. J. R. has been funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 853368). A. D. acknowledges support of the Russian Science Foundation (Project No. 17-12-01587).

Publisher Copyright:
© 2022 American Physical Society.

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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