Real-space renormalization study of disordered interacting bosons

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Abstract
We study a real-space renormalization group for disordered, interacting bosons at zero temperature in one and two dimensions. In the absence of disorder at commensurate density we find a superfluid–Mott insulator transition that is unaffected by the addition of weak disorder, i.e., disorder is weakly irrelevant at the Mott-superfluid transition. Above a threshold disorder a gapless insulating phase—the ‘‘Bose glass’’—intervenes.