Large-N renormalization-group study of the commensurate dirty-boson problem.

We use a large N renormalization group (RG) method to study a model of interacting boson system with a quenched random potential. In the absence of impurities , the pure boson system has a critical point that describes the superfluid-Mott-insulator (SF-MI) transition. The SF-MI transition of d dimensional bosons belongs to the (d + 1) dimensional XY model universality class. In this paper, we study the dirty-boson critical points in the neighborhood of this pure SF-MI critical point. In general, the on-site random potential in the original lattice model gives two types of randomness in the effective field theoretic action. One is the randomness in the effective on-site repulsion w(x) and the other is the randomness of the chemical potential u(x). It turns out that d = 2 is the critical dimension for both types of disorder but the roles of these two types of disoder are reversed as d = 2 is crossed. Applying ǫ = d − 2 expansion, we found coupled RG equations for both kinds of randomness which reveal several non-trivial critical points. All the weak random fixed points we found have three or more relevant directions. We conclude that the direct SF-MI transition is unlikely to occur near two dimensions.