Mott criticality in electric transport of triangular lattice Hubbard model

We numerically study electric transport near the Mott metal-insulator transition for the half-filled Hubbard model on a triangular lattice. Our approach is a cellular dynamical mean field theory (CDMFT) with a continuous-time QMC solver and we calculate optical conductivity including vertex corrections. The main issue is the variation of optical conductivity upon controlling Coulomb repulsion $U$ for various temperatures. Near the Mott critical end point, a Drude peak on the metallic side smoothly continues to an ``ingap" peak emerging within the Hubbard gap on the insulating side. We find a critical power-law behavior in their $U$-dependence near the critical point. The obtained critical exponent $1/\delta=0.15$ of the optical weight differs from the exponent $1/\delta=1/3$ of the order parameter (double occupancy) in the CDMFT calculations. This discrepancy suggests that conductivity does not have the same scaling behavior as that for the order parameter[1]. [1]T. Sato, K. Hattori, and H. Tsunetsugu, J. Phys. Soc. Jpn. $\bf 81$, 083703 (2012).