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

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.

Superfluid density and quasi-long-range order in the one-dimensional disordered Bose–Hubbard model

“…Although this picture is qualitatively wellunderstood, the full quantitative characterization of the disordered Bose-Hubbard model remains challenging: considerable efforts have been devoted to study its phase diagram, in particular the location and the nature of the glassy phase [23][24][25][26][27][28][29][30][31][32][33][34]. Developments on the issue, with a special emphasis on numerical simulations, have been reviewed in [35]. Recently, an experiment with optical lattices has made an important step forward in mapping the phase diagram from weak to strong interactions [36].…”

Superfluid/Bose-glass transition in one dimension

“…. S denotes the average with respect to the action S. Combining the last two expressions for W (J) we obtain exp(Jϕ) S expressed in powers of the anharmonic coupling g. Now we use the expressions (65) and (66) for our model (9). We should have in mind that the above derivation is written in shorthand notation where we suppressed all internal indices (e.g., replica indices) and GJ is determined by the structure of the theory.…”

“…Further analyses of the transition in terms of vortex proliferation 4 confirmed and generalized this result and numerical studies of disordered bosons [5][6][7] confirmed both the reentrant nature of the phase diagram and the nature of the moderate interaction transition. 8,9 Extensions of this transition to finite temperature have also recently attracted a great deal of attention.…”

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

“…The Bose-Hubbard model with different forms of diagonal disorder has been reviewed in [34] while random onsite interactions have been considered in [35] It has been shown recently that the simple BoseHubbard description for fermion-boson mixture may not be adequate for stronger interspecies interactions. The shift of the observed transition between the superfluid (SF) and the MI phases, observed experimentally in Refs.…”