Direct Mott Insulator-to-Superfluid Transition in the Presence of Disorder

TL;DR

This paper develops a new renormalization group theory to analyze quantum phase transitions in disordered bosonic systems, revealing conditions for direct Mott insulator-to-superfluid transitions and the nature of intermediate phases.

Contribution

It introduces a novel RG approach to distinguish between direct and two-step transitions in disordered bosonic systems across different dimensions.

Findings

Direct transition in weak disorder for d>4

Transition survives only at commensurate filling for 2<=d<4

Two fixed points describe separate transitions under strong disorder

Abstract

We introduce a new 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 > 4 a finite region around the particle-hole symmetric point supports this direct transition, whereas for 2=< d <4 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.