Universal conductivity in the boson Hubbard model in a magnetic field

The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical $XY$-model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of magnetic field is characterized by the frustration $f$. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent $z$, the correlation length exponent $\nu$, and the universal conductivity $\sigma^*$. For the disorder-free model with $f=1/2$, we obtain $z \approx 1$, $1/\nu \approx 1.5$, and $\sigma^*/\sigma_Q =0.52 \pm 0.03 $ where $\sigma_Q$ is the quantum conductance. We also study the case with $f=1/3$, in which we find $\sigma^*/\sigma_Q = 0.83 \pm 0.06 $. The value of $\sigma^*$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find $z=1.07 \pm 0.03$, $\nu \approx 1$, and $\sigma^*/\sigma_Q= 0.27 \pm 0.04$ for the case $f=0$, and $z=1.14 \pm 0.03$, $\nu \approx 1$, and $\sigma^*/\sigma_Q= 0.49 \pm 0.04$ for the case $f=1/2$.