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.Comment: To appear in the Proceedings of the conference Particle systems and PDE's - II, held at the Center of Mathematics of the University of Minho in December 201

Dynamics in many-body localized quantum systems without disorder

We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration is nonperturbatively slow in the hopping strength, and potentially genuinely nonergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, which are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with the system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonan