Universal conductivity in the two-dimensional boson Hubbard model

We use quantum Monte Carlo methods to evaluate the conductivity σ of the two-dimensional disordered boson Hubbard model at the superfluid–Bose-glass phase boundary. At the critical point for particle density ρ=0.5, we find ${\mathrm{\sigma }}_{\mathit{c}}$=(0.45±0.07)${\mathrm{\sigma }}_{\mathit{Q}}$, where ${\mathrm{\sigma }}_{\mathit{Q}}$=${\mathit{e}}_{\mathrm{*}}^2$/h from a finite-size scaling analysis of the superfluid density. We obtain ${\mathrm{\sigma }}_{\mathit{c}}$=(0.47±0.08)${\mathrm{\sigma }}_{\mathit{Q}}$ from a direct calculation of the current-current correlation function. Simulations at the critical points for other particle densities, ρ=0.75 and 1.0, give similar values for σ. We discuss possible origins of the difference in this value from that recently obtained by other numerical approaches.