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 the 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 ν, and the universal conductivity ${\mathrm{\sigma }}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z≊1, 1/ν≊1.5, and ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.52±0.03, where ${\mathrm{\sigma }}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.83±0.06. The value of ${\mathrm{\sigma }}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07±0.03, ν≊1, and ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.27±0.04 for the case f=0, and z=1.14±0.03, ν≊1, and ${\mathrm{\sigma }}^{\mathrm{*}}$/${\mathrm{\sigma }}_{\mathit{Q}}$=0.49±0.04 for the case f=1/2.