Eigenstate thermalization hypothesis and integrals of motion

TL;DR

This paper investigates how local integrals of motion influence the eigenstate thermalization hypothesis, proposing a method to reduce fluctuations in local observable matrix elements and validating it through numerical analysis.

Contribution

It introduces a systematic protocol to construct observables that minimizes fluctuations by accounting for LIOMs, bridging the gap between ETH and integrable systems.

Findings

Nonvanishing fluctuations indicate the presence of LIOMs.

The proposed protocol reduces fluctuations and structure of diagonal matrix elements.

Numerical results confirm the effectiveness of the method in different models.

Abstract

Even though foundations of the eigenstate thermalization hypothesis (ETH) are based on random matrix theory, physical Hamiltonians and observables substantially differ from random operators. One of the major challenges is to embed local integrals of motion (LIOMs) within the ETH. Here we focus on their impact on fluctuations and structure of the diagonal matrix elements of local observables. We first show that nonvanishing fluctuations entail the presence of LIOMs. Then we introduce a generic protocol to construct observables, subtracted by their projections on LIOMs as well as products of LIOMs. The protocol systematically reduces fluctuations and/or the structure of the diagonal matrix elements. We verify our arguments by numerical results for integrable and nonintegrable models.