Can translation invariant systems exhibit a Many-Body Localized phase?

TL;DR

This paper reviews recent research on the potential for many-body localization in systems without quenched disorder, arguing that such systems can show signs of asymptotic localization but not true localization.

Contribution

It provides theoretical arguments and evidence suggesting that disorder-free systems can exhibit localized behavior without achieving genuine many-body localization.

Findings

Disorder-free systems can show asymptotic localization.

Genuine many-body localization likely requires quenched disorder.

Theoretical evidence distinguishes between asymptotic and true localization.

Abstract

This note is based on a talk by one of us, F. H., at the conference PSPDE II, Minho 2013. We review some of our recent works related to (the possibility of) Many-Body Localization in the absence of quenched disorder (in particular arXiv:1305.5127,arXiv:1308.6263,arXiv:1405.3279). In these works, we provide arguments why systems without quenched disorder can exhibit `asymptotic' localization, but not genuine localization.