Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis

• URL: http://arxiv.org/abs/2303.03448v1
• Date: Mon, 6 Mar 2023 19:17:15 GMT
• Title: Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Authors: Giorgio Cipolloni, Jonah Kudler-Flam
• Abstract summary: Eigenstate Thermalization Hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. We investigate what extent the ETH holds in non-Hermitian many-body systems. We come to the surprising conclusion that the fluctuations between eigenstates is of equal order to the average, indicating no thermalization.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Eigenstate Thermalization Hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. The ETH asserts that expectation values of simple observables in energy eigenstates are accurately described by smooth functions of the thermodynamic parameters, with fluctuations and off-diagonal matrix elements exponentially suppressed in the entropy. We investigate to what extent the ETH holds in non-Hermitian many-body systems and come to the surprising conclusion that the fluctuations between eigenstates is of equal order to the average, indicating no thermalization. We support this conclusion with mathematically rigorous results in the Ginibre ensemble and numerical results in other ensembles, including the non-Hermitian Sachdev-Ye-Kitaev model, indicating universality in chaotic non-Hermitian quantum systems.

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