The Two-Dimensional Disordered Boson Hubbard Model: Evidence for a Direct Mott Insulator-to-Superfluid Transition and Localization in the Bose Glass Phase

TL;DR

This study uses Monte Carlo simulations to analyze the disordered boson Hubbard model in two dimensions, revealing a direct transition from Mott insulator to superfluid and localized excitations in the Bose glass phase, with critical exponents matching the 3D XY model.

Contribution

It provides evidence for a direct Mott insulator-to-superfluid transition without an intervening Bose glass phase at weak disorder in 2D, and characterizes localization and critical behavior.

Findings

Bose glass phase exhibits a $1/\chi^2$ tail in local susceptibility distribution.

Excitations in the Bose glass are fully localized, with established scaling laws.

Critical exponents match those of the classical 3D XY model, indicating disorder irrelevance at the Mott lobe tip.

Abstract

We investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is found to have a $1/ \chi^2$ tail and the imaginary time Green's function decays algebraically $C(\tau) \sim \tau^{-1}$, giving rise to a divergent global susceptibility. By considering the participation ratio it is shown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensurate boson densities we find a direct Mott insulator to superfluid transition without an intervening Bose glass phase for weak disorder. For this transition we obtain the critical exponents $z=1, \nu=0.7\pm 0.1$ and $\eta = 0.1 \pm 0.1$, which agree with those for the classical three-dimensional XY model without disorder. This indicates that disorder is irrelevant at the tip of the Mott-lobes and that here the inequality $\nu\ge2/d$ is violated.