$\epsilon$-Expansion of the Conductivity at the Superconductor-Mott Insulator Transition

TL;DR

This paper calculates the universal conductivity at the superconductor-Mott insulator transition using epsilon-expansion, providing results consistent with Monte Carlo simulations.

Contribution

It presents the epsilon-expansion calculation of the conductivity at the transition to order epsilon squared, including the universal conductance in two dimensions.

Findings

Derived the frequency-dependent conductivity scaling form.

Calculated the epsilon-expansion of the prefactor to order epsilon^2.

Found the universal conductance in 2D to be approximately 0.315 (4e^2/h).

Abstract

We study the critical behavior of the conductivity $\sigma(\omega)$ at the zero temperature superconductor-Mott insulator transition in $d$ space-time dimensions for a model of bosons with short-range interaction and no disorder. We obtain $\sigma(\omega_n ) = (4e^2/\hbar) \sigma_{\epsilon} \omega_n^{1-\epsilon}$, as predicted by the scaling theory, and the prefactor $\sigma_{\epsilon}$ is calculated in the $\epsilon$-expansion, to order $\epsilon ^2$ ($\epsilon = 4-d$). In two spatial dimensions, ($d=3$), we find a value of the universal conductance $\sigma^\star =0.315 (4e^2/h)$, in good agreement with the known Monte Carlo results.