Universal Conductivity in the Two dimensional Boson Hubbard Model

TL;DR

This study uses Quantum Monte Carlo simulations to determine the universal conductivity at the superfluid-bose glass transition in a 2D disordered boson Hubbard model, finding consistent values across different densities.

Contribution

First precise numerical estimate of the universal conductivity at the superfluid-bose glass transition in 2D disordered boson systems.

Findings

Universal conductivity at critical point: approximately 0.45 times quantum of conductance.

Consistent conductivity values across different particle densities.

Comparison and discussion of differences with other numerical methods.

Abstract

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