A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder

TL;DR

This review discusses the phase diagram of the disordered Bose-Hubbard model, highlighting the Bose glass phase, phase transitions, and recent Monte Carlo simulation results in 2D and 3D systems.

Contribution

It synthesizes analytical and Monte Carlo simulation results to clarify the phase structure and transitions in the disordered Bose-Hubbard model across different dimensions.

Findings

Bose glass phase intervenes between superfluid and Mott insulator.

Phase transition line near the Mott lobe tip is insensitive to disorder.

Phase diagrams in 2D and 3D are comprehensively discussed.

Abstract

We review the physics of the Bose-Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.