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

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 intrachain ( t ) and interchain ( t ′ ) hoppings. We find that the phase diagram as a function of the boson density, disorder strength, and t ′ / t is far from being trivial. This contrasts with the case of spinless 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.