Optical conductivity of the Hubbard model at finite temperature

Abstract

The optical conductivity, $σ(ω)$, of the two dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane d.c. resistivity, $ρ_{ab}$, is also evaluated. We find that at large U/t and temperature T, $ρ_{ab}$ is approximately linear with temperature, in reasonable agreement with experiments on high-T$_c$ superconductors. Moreover, we note that $σ(ω)$ displays charge excitations, a mid-infrared (MIR) band and a Drude peak, also as observed experimentally. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than $1/ω^2$ at energies smaller than the insulator gap near half-filling.