$ε$-Expansion of the Conductivity at the Superconductor-Mott Insulator Transition

Abstract

We study the critical behavior of the conductivity $σ(ω)$ 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 $σ(ω_n ) = (4e^2/\hbar) σ_ε ω_n^{1-ε}$, as predicted by the scaling theory, and the prefactor $σ_ε$ is calculated in the $ε$-expansion, to order $ε^2$ ($ε= 4-d$). In two spatial dimensions, ($d=3$), we find a value of the universal conductance $σ^\star =0.315 (4e^2/h)$, in good agreement with the known Monte Carlo results.