Direct Mott insulator-to-superfluid transition in the presence of disorder

We use renormalization-group theory to examine the quantum phase transitions upon exiting the insulating phase of a disordered, strongly interacting boson system. For weak disorder we find a direct transition from this Mott insulator to the superfluid phase. In $d>\mathrm{}4\mathrm{}$ a finite region around the particle-hole symmetric point supports this direct transition, whereas for $2<~d<\mathrm{}4\mathrm{}$ perturbative arguments suggest that the direct transition survives only precisely at commensurate filling. For strong disorder the renormalization trajectories pass next to two fixed points, describing a pair of distinct transitions; first 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 dimension $d$.