Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"

TL;DR

This paper critiques a recent claim about constructing Hamiltonians that violate the eigenstate thermalization hypothesis, clarifying the importance of symmetry sectors in ETH validity.

Contribution

It clarifies a misunderstanding in prior work by emphasizing the role of symmetry sectors in the eigenstate thermalization hypothesis.

Findings

Mixing symmetry sectors affects ETH validity.

The critique clarifies the conditions under which ETH applies.

Misinterpretation of ETH assumptions can lead to incorrect conclusions.

Abstract

In a recent Letter [PhysRevLett.119.030601 (2017), arXiv:1702.08227], Shiraishi and Mori claim to provide a general method for constructing local Hamiltonians that do not exhibit eigenstate thermalization. We argue that the claim is based on a misunderstanding of the eigenstate thermalization hypothesis (ETH). More specifically, on the assumption that ETH is valid for the entire Hamiltonian matrix instead of each symmetry sector independently. We discuss what happens if one mixes symmetry sectors in the two-dimensional transverse field Ising model.