Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis

TL;DR

This paper numerically investigates the eigenstate thermalization hypothesis (ETH) in quantum systems, revealing universal behavior and confirming ETH even in near-integrable systems through large deviation analysis.

Contribution

It introduces a large deviation approach to test ETH, demonstrating its validity and universal features in finite-size quantum systems, including near-integrable cases.

Findings

Confirmed strong ETH in near-integrable systems

Finite-size scaling of athermal states is double exponential

Large deviation analysis is effective for studying thermalization

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, where we found that the finite-size scaling of the ratio of athermal eigenstates is double exponential. Our result illuminates universal behavior of quantum chaos, and suggests that large deviation analysis would serve as a powerful method to investigate thermalization in the presence of the large finite-size effect.