"Universal Superfuid Transition and Transport Properties of Two-Dimensional Dirty Bosons"

The interplay of disorder and interactions has been at the center of intense theoretical and experimental activity the past decades. It sustains rich phase diagrams, relevant to a wide range of condensed-matter systems. Recent evelopments with ultracold atoms spark a renewed interest and open new challenging issues. For instance, in interacting systems on the continuum, the intervening phases are largely debated and still in a conjectural stage. In this talk I will discuss the phase diagram of disordered and interacting ultracold atoms in two dimensions, that we have obtained thanks to accurate, large-scale Quantum Monte Carlo simulations.[I] I will show that the superfuid transition is strongly protected against disorder, up to the zero-temperature Bose-glass transition. Most of its critical properties can be understood in terms of an universal BKT description with a simple scaling of the critical temperature versus the disorder strength. I will then address the strongly disordered regime at finite temperature where the possible existence of a (many-body) localized phase constitutes a challenging open question. Thanks to a taylored methodological improvement, we have gained direct access to the conducting properties. I will show that the finite-temperature insulating phase merging at large disorder strength is well described by a thermally activated behavior of the Arrhenius type.