The superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model

TL;DR

This study uses quantum Monte Carlo simulations to precisely determine the superfluid-insulator transition point in a disordered two-dimensional Bose-Hubbard model, revealing how disorder affects the phase boundary and universal properties.

Contribution

It provides the first large-scale disorder averaging in this context, accurately locating the critical point and analyzing universal scaling behavior in the presence of disorder.

Findings

Disorder enlarges the superfluid region compared to the clean system.

Critical hopping parameter in the disordered case is significantly lower than in the clean case.

Universal dynamic conductivity scaling curves are obtained at the critical point.

Abstract

We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder and the quantum critical point between the Bose-glass and superfluid is determined in both the grand canonical ($\mu/U=0.375$ close to $\rho=1$) and canonical ensemble ($\rho=1$ and 0.5). Particular attention is paid to disorder averaging and it is shown that an extremely large number of disorder realizations are needed in order to obtain reliable results. Typically we average over more than $100,000$ disorder realizations. In the grand canonical ensemble we find $Z t_c/U=0.112(1)$ with $\mu/U=0.375$, significantly different from previous studies. When compared to the critical point in the absence of disorder ($Z t_c/U=0.2385$), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point, in order to estimate universal features, we compute the dynamic conductivity scaling curves.