Eigenstate Correlations, Thermalization and the Butterfly Effect
Amos Chan, Andrea De Luca, J. T. Chalker
TL;DR
This paper explores eigenstate correlations in ergodic quantum systems, revealing universal structures beyond ETH through numerical studies of Floquet circuits, enhancing understanding of thermalization and quantum chaos.
Contribution
It identifies universal eigenstate correlation structures beyond ETH in Floquet systems and validates them with numerical simulations.
Findings
Eigenstate correlations exhibit universal long-distance structure.
ETH accurately describes many eigenstate properties.
Additional correlations beyond ETH are numerically confirmed.
Abstract
We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to give an excellent description of these quantities, the butterfly effect implies structure beyond ETH. We determine the universal form of this structure at long distances and small eigenvalue separations for Floquet systems. We use numerical studies of a Floquet quantum circuit to illustrate both the accuracy of ETH and the existence of our predicted additional correlations.
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