Many-body localized (MBL) systems, i.e. systems that do not thermally equilibrate
under their own dynamics but rather evolve in such a way that the memory
about local features of the initial state is preserved, have recently received
a lot of attention. We consider a system of ultracold atoms in one-dimensional optical
lattice with disordered on-site interparticle interactions. The MBL is found to occur in
the system as one increases the interactions.
The single-particle extended states are eigenstates in the absence of the disorder.
Therefore, the observed localization is an inherent effect of the interactions and thus
a genuine many-body effect. The localization is inspected by means
of eigenvalue statistics as well as by time propagation of initial states with density wave order.

arXiv:1607.00227, PRL submitted