DIRECT MOTT INSULATOR TO SUPERFLUID TRANSITION IN THE PRESENCE OF DISORDER

We use renormalization-group theory to examine the quantum phase trans itions upon exiting the insulating phase of a disordered, strongly int eracting boson system. For weak disorder we End a direct transition fr om this Mott insulator to the superfluid phase. In d>4 a finite region around the particle-hole symmetric point supports this direct transit ion, whereas for 2 less than or equal to d<4 perturbative arguments su ggest that the direct transition survives only precisely at commensura te filling. For strong disorder the renormalization trajectories pass next to two fixed points, describing a pair of distinct transitions; f irst from the Mott insulator to the Bose glass, and then from the Bose glass to the superfluid. The latter fixed point possesses statistical particle-hole symmetry and a dynamical exponent z, equal to the dimen sion d.