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Eigenstate Correlations, Thermalization, and the Butterfly Effect
Amos Chan1, Andrea De Luca1, J T Chalker1
1Theoretical Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom.
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 phenomenon of scrambling and the butterfly effect imply 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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