Optical conductivity from cluster DMFT: Formalism and application to high-Tc superconductors

The optical conductivity of the one-band Hubbard model is calculated using the ``dynamical cluster approximation'' implementation of dynamical mean field theory for parameters appropriate to high-temperature copper-oxide superconductors. We present a scheme for obtaining the vertex corrections and show their significant contributions especially to the conductivity of undoped and lightly doped materials where it strongly affects the above-gap absorption. For parameters $U=9t$ and $t'=-0.3t$ relevant to high temperature superconductors, at densities of one electron per site an insulating state is found with a gap $\sim$ 1.8eV similar in magnitude to that observed in La$_2$CuO$_4$. On doping, the gap is rapidly destabilized and absorption appears at low frequencies, again in a manner consistent with the measurements. The mid-infrared feature observed at intermediate dopings is shown to arise from a pseudogap structure in the density of states.