Superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model

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 the grand canonical ensemble at $\ensuremath{\mu}/U=0$ (close to $\ensuremath{\rho}=0.5$), $\ensuremath{\mu}/U=0.375$ (close to $\ensuremath{\rho}=1$), and $\ensuremath{\mu}/U=1$ as well as in the canonical ensemble at $\ensuremath{\rho}=0.5$ and 1. Particular attention is paid to disorder averaging, and it is shown that a large number of disorder realizations are needed in order to obtain reliable results. Typically, more than $100\phantom{\rule{0.16em}{0ex}}000$ disorder realizations were used. In the grand canonical ensemble, we find $Z{t}_{c}/U=0.112(1)$ with $\ensuremath{\mu}/U=0.375$, 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, we then study the dynamic conductivity.