Many-body delocalization of ultracold bosons in lattices

Many-body localization describes the phenomenon of localization and vanishing charge transport in closed quantum many-body systems. It is well accepted by now that MBL is stable in one dimension and many of its properties have been revealed. Much less is known in two dimensions. Here we present our recent results on the study of the stability of the localization in 2d bosonic lattice systems. Our observation is consistent with persistent localization if the system is brought in contact with a small quantum bath, but localization is clearly destroyed for larger baths. The dynamics towards the steady state differs strongly in the two cases.