Comment on "Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined" [arXiv:0810.3720]

TL;DR

This paper critiques a previous claim that thermalization in Bose-Hubbard systems after a quench is due to an approximate Boltzmann distribution of overlaps, showing instead that overlaps do not generally follow such distributions.

Contribution

It challenges the explanation that thermalization arises from overlap distributions resembling canonical or microcanonical ensembles in quantum quenches.

Findings

Overlap distributions are generally not related to canonical distributions.

The proposed explanation for thermalization in the original paper is not supported.

Overlap distributions do not explain thermalization in quantum many-body systems.

Abstract

In a recent paper Roux [Phys. Rev. A 79, 021608(R) (2009), arXiv:0810.3720] argued that thermalization in a Bose-Hubbard system, after a quench, follows from the approximate Boltzmann distribution of the overlap between the initial state and the eigenstates of the final Hamiltonian. We show here that the distribution of the overlaps is in general not related to the canonical (or microcanonical) distribution and, hence, it cannot explain why thermalization occurs in quantum systems.