The electrical conductivity of an amorphous Hubbard model

We study the frequency-dependent electrical conductivity of a structurally disordered single-band Hubbard model near half-filling and in the strong-correlation limit. The electronic transfer integral is assumed to have a quasi-exponential form as used in the impurity-band problem of doped semiconductors. The short-time expansion of the current correlation function is calculated diagrammatically to the second order in the inverse temperature β and up to the seventh order in electronic hopping. Based on this expansion an approximate current correlation function is constructed. By means of the Kubo formula, the configurational average of the electrical conductivity is then calculated to order β2 for various atomic densities. The validity of the high-temperature expansion is examined. We also study the effect of spin polarization on the absorption line shape and the dc resistivity at different temperatures.