Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.

László Erdős, Volodymyr Riabov
Author Information
  1. László Erdős: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria. ORCID
  2. Volodymyr Riabov: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria. ORCID

Abstract

We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure.

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