Phase diagram of the disordered Bose-Hubbard model

TL;DR

This paper maps the complex phase diagram of the disordered 3D Bose-Hubbard model, revealing a robust superfluid phase, the intervening Bose glass, and the nature of phase transitions, with implications for cold-atom experiments.

Contribution

It provides the first detailed phase diagram of the disordered 3D Bose-Hubbard model, clarifying the nature of phase transitions and the robustness of superfluidity under strong disorder.

Findings

Bose glass always intervenes between Mott insulator and superfluid phases.

Superfluid phase persists under disorder nearly 50 times the particle bandwidth.

The phase diagram features a long superfluid finger at strong disorder and interactions.

Abstract

We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling, which has been controversial for many years. The theorem of inclusions, proven in Ref. [1], states that the Bose glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical point is due to a zero concentration of rare regions where extreme fluctuations of disorder mimic a {\it regular} gapless system. An exactly solvable random transverse field Ising model in one dimension is used to illustrate the point. A highly non-trivial overall shape of the phase diagram is revealed with the worm algorithm. The phase diagram features a long superfluid finger at strong disorder and on-site interaction. Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth. Finally, we comment on the feasibility of obtaining this phase diagram in cold-atom experiments, which work with trapped systems at finite temperature.