Bose-glass, superfluid, and rung-Mott phases of hard-core bosons in disordered two-leg ladders

TL;DR

This study uses Monte Carlo methods to explore how disorder affects phases of hard-core bosons in a disordered two-leg ladder, revealing complex phase transitions and the prevalence of Bose-glass phases.

Contribution

It provides a detailed phase diagram showing the effects of disorder and inter-chain coupling on bosonic phases, highlighting differences from fermionic localization.

Findings

Bose-glass phase always appears between Mott insulator and superfluid.

Direct transition from rung-Mott insulator to superfluid occurs only in clean systems.

Disorder induces Bose-glass phases surrounding Mott insulators.

Abstract

By means of Monte Carlo techniques, we study the role of disorder on a system of hard-core bosons in a two-leg ladder with both intra-chain ($t$) and inter-chain ($t^\prime$) hoppings. We find that the phase diagram as a function of the boson density, disorder strength, and $t^\prime/t$ is far from being trivial. This contrasts the case of spin-less fermions where standard localization arguments apply and an Anderson-localized phase pervades the whole phase diagram. A compressible Bose-glass phase always intrudes between the Mott insulator with zero (or one) bosons per site and the superfluid that is stabilized for weak disorder. At half filling, there is a direct transition between a (gapped) rung-Mott insulator and a Bose glass, which is driven by exponentially rare regions where disorder is suppressed. Finally, by doping the rung-Mott insulator, a direct transition to the superfluid is possible only in the clean system, whereas the Mott phase is always surrounded by the a Bose glass when disorder is present. The phase diagram based on our numerical evidence is finally reported.