Universal conductivity in the boson Hubbard model in a magnetic field

Abstract

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 ${\sigma }^{\ast }$. For the disorder-free model with $f=1/2$, we obtain $z\approx 1$, $1/\nu \approx 1.5$, and ${\sigma }^{\ast }/{\sigma }_Q=0.52\pm 0.03$ where ${\sigma }_Q$ is the quantum conductance. We also study the case with $f=1/3$, in which we find ${\sigma }^{\ast }/{\sigma }_Q=0.83\pm 0.06$. The value of ${\sigma }^{\ast }$ 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 ${\sigma }^{\ast }/{\sigma }_Q=0.27\pm 0.04$ for the case $f=0$, and $z=1.14\pm 0.03$, $\nu \approx 1$, and ${\sigma }^{\ast }/{\sigma }_Q=0.49\pm 0.04$ for the case $f=1/2$.

26 pages (9 pages for figures), postscript, RANU1

References in corpus (2)

• Universal Conductivity in the Two dimensional Boson Hubbard Model
• Flux Pinning and Phase Transitions in Model High-Temperature Superconductors with Columnar Defects

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