Reply to "Comment on "Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis"" by Mondaini et.al

TL;DR

This paper defends a specific formulation of the eigenstate thermalization hypothesis (ETH), clarifying its properties and roles in thermalization, and argues that their results are qualitatively new and unexpected.

Contribution

The paper distinguishes diagonal and off-diagonal ETH in different sectors, clarifies their roles, and defends the novelty of their ETH formulation in thermalization studies.

Findings

Clarifies properties of diagonal and off-diagonal ETH

Highlights roles of ETH sectors in thermalization

Argues for the novelty of their ETH results

Abstract

This paper is a Reply paper to the Comment paper by Mondaini et.al. [arXiv:1711.06279]. We first distinguish the diagonal and the off-diagonal eigenstate thermalization hypothesis (ETH) in each sector and in the whole Hilbert space, and then clarify their properties and their roles in thermalization. We argue that our formulation of the ETH in our letter is a standard and natural one in the context of thermalization, and that our results are qualitatively new and unexpected.