Universal conductivity in the boson Hubbard model in a magnetic field

TL;DR

This study uses Monte Carlo simulations to analyze the universal conductivity at the superconductor-insulator transition in the 2D boson Hubbard model, considering magnetic fields and disorder effects.

Contribution

It provides new numerical estimates of universal conductivity and critical exponents in the boson Hubbard model under magnetic fields and disorder, extending previous theoretical predictions.

Findings

Universal conductivity varies with magnetic frustration f.

Disorder affects the critical exponents and conductivity values.

Results align with Gaussian model estimates for certain cases.

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 $\sigma^*$. 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 $f=1/2$.