Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition

TL;DR

This study investigates the universal scaling behavior of conductivity at the superfluid-insulator quantum phase transition in two dimensions, revealing a crossover from w_k-scaling to w/T-scaling at finite temperature.

Contribution

It provides the first detailed numerical analysis of conductivity scaling at finite temperature in the thermodynamic limit, showing a universal dc conductivity different from zero-temperature estimates.

Findings

Conductivity scales with w/T at low frequencies and temperatures.

Universal dc conductivity estimated at approximately 0.45 Q^2/h.

Deviations from previous zero-temperature scaling predictions.

Abstract

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from w_k-scaling of the conductivity towards w_k/T-scaling at low Matsubara frequencies w_k. By careful analytic continuation using Pade approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with w/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be 0.45(5)Q^2/h, distinct from previous estimates in the T=0, w/T >> 1 limit.