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Numerical Large Deviation Analysis of the Eigenstate Thermalization Hypothesis
Toru Yoshizawa1, Eiki Iyoda1, Takahiro Sagawa1
1Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
Abstract:
A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have thermal properties. We numerically investigate the ETH by focusing on the large deviation property, which directly evaluates the ratio of athermal energy eigenstates in the energy shell. As a consequence, we have systematically confirmed that the strong ETH is indeed true even for near-integrable systems. Furthermore, we found that the finite-size scaling of the ratio of athermal eigenstates is a double exponential for nonintegrable systems. Our result illuminates the universal behavior of quantum chaos, and suggests that a large deviation analysis would serve as a powerful method to investigate thermalization in the presence of the large finite-size effect.
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