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Eigenstate Thermalization and Rotational Invariance in Ergodic Quantum Systems.

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Generic rotationally invariant matrix models satisfy a simple relation: the probability distribution of half the difference between any two diagonal elements and the one of off-diagonal elements are the same.… Click to show full abstract

Generic rotationally invariant matrix models satisfy a simple relation: the probability distribution of half the difference between any two diagonal elements and the one of off-diagonal elements are the same. In the spirit of the eigenstate thermalization hypothesis, we test the hypothesis that the same relation holds in quantum systems that are nonlocalized, when one considers small energy differences. The relation provides a stringent test of the eigenstate thermalization hypothesis beyond the Gaussian ensemble. We apply it to a disordered spin chain, the Sachdev-Ye-Kitaev model, and a Floquet system.

Keywords: rotational invariance; eigenstate thermalization; thermalization; invariance ergodic; quantum systems; thermalization rotational

Journal Title: Physical review letters
Year Published: 2019

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