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

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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 wₖ-scaling of the conductivity towards wₖ/T-scaling at low Matsubara frequencies wₖ. 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)Q²/h, distinct from previous estimates in the T=0, w/T >> 1 limit.