Eigenstate thermalization and rotational invariance in ergodic quantum systems

Abstract

Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the Eigenstate Thermalization Hypothesis (ETH), we test the hypothesis that the same relation holds in quantum systems that are non-localized, when one considers small energy differences. The relation provides a stringent test of ETH beyond the Gaussian ensemble. We apply it to a disordered spin chain, the SYK model and a Floquet system.

5 pages, 4 figures

References in corpus (4)

• Anomalous thermalization in ergodic systems
• Introduction to Random Matrices - Theory and Practice
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries

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