Superfluid-insulator transition of disordered bosons in one-dimension

TL;DR

This paper investigates the superfluid-insulator transition in one-dimensional disordered bosonic systems using a non-perturbative real space renormalization group, revealing a universal KT-like transition with disorder-dependent critical properties.

Contribution

It introduces a strong randomness RG approach that captures the full phase diagram and uncovers a new universality class with disorder-dependent critical Luttinger parameters.

Findings

Transition is always KT-like with diverging scales.

Critical Luttinger parameter depends on disorder strength.

Identifies three distinct insulating phases based on disorder type.

Abstract

We study the superfluid-insulator transition in a one dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong randomness real space renormalization group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid insulator transition is always Kosterlitz- Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a non universal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. {\bf 3}, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott glass phase. If both integer and half integer filling factors are allowed then the corresponding phase is a random singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.