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The optical conductivity of the one-band Hubbard model is calculated usingthe 'Dynamical Cluster Approximation' implementation of dynamical mean fieldtheory for parameters appropriate to high temperature copper-oxidesuperconductors. The calculation includes vertex corrections and the resultdemonstrates their importance. At densities of one electron per site, aninsulating state is found with gap value and above-gap absorption consistentwith measurements. As carriers are added the above gap conductivity rapidlyweakens and a three component structure emerges, with a low frequency 'Drude'peak, a mid-infrared absorption, and a remnant of the insulating gap. Themid-infrared feature obtained at intermediate dopings is shown to arise from apseudogap structure in the density of states. On further doping theconductivity evolves to the Drude peak plus weakly frequency dependent tailstructure expected for less strongly correlated metals.

Optical conductivity in cluster dynamical mean field theory: formalism and application to high temperature superconductors