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

Understand

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.