Universal Conductivity in the Two dimensional Boson Hubbard Model

Abstract

We use Quantum Monte Carlo to evaluate the conductivity $σ$ of the 2--dimensional disordered boson Hubbard model at the superfluid-bose glass phase boundary. At the critical point for particle density $ρ=0.5$, we find $σ_{c}=(0.45 \pm 0.07) σ_{Q}$, where $σ_{Q}= e_{*}^{2} / h$ from a finite size scaling analysis of the superfluid density. We obtain $σ_{c}=(0.47 \pm 0.08) σ_{Q}$ 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.