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

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 $\sigma ({\omega }_n)=(4e^2/\hslash ){\sigma }_{\epsilon }{\omega }_n^{1-\epsilon }$, 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.

8 pages REVTEX

References in corpus (1)

• Universal Conductivity in the Two dimensional Boson Hubbard Model

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