Can translation invariant systems exhibit a Many-Body Localized phase?
  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. 
Wojciech De Roeck and Fran\c{c}ois Huveneers
cond-mat.stat-mech