Optical conductivity of a metal-insulator transition for the Anderson-Hubbard model in three dimensions away from half filling

The Anderson-Hubbard model is considered to be the least complicated model using lattice fermions with which one can hope to study the physics of transition-metal oxides with spatial disorder. We have completed a numerical investigation of this model for three-dimensional simple-cubic lattices using a real-space self-consistent Hartree-Fock decoupling approximation for the Hubbard interaction. In this formulation we treat the spatial disorder exactly and therefore we account for effects arising from localization physics. We have examined the model for electronic densities well away from 1/2 filling thereby avoiding the physics of a Mott insulator. Several recent studies have made clear that the combined effects of electronic interactions and spatial disorder can give rise to a suppression of the electronic density of states and a subsequent metal-insulator transition can occur. We supplement such studies by calculating the ac conductivity for such systems. Our numerical results show that weak interactions enhance the density of states at the Fermi level and the low-frequency conductivity, there are no local magnetic moments, and the ac conductivity is Drude like. However, with a large enough disorder strength and larger interactions the density of states at the Fermi level and the low-frequency conductivity are both suppressed, the conductivity becomes non-Drude like, and these phenomena are accompanied by the presence of local magnetic moments. The low-frequency conductivity changes from a $\ensuremath{\sigma}\ensuremath{-}{\ensuremath{\sigma}}_{\text{dc}}\ensuremath{\sim}{\ensuremath{\omega}}^{1/2}$ behavior in the metallic phase, to a $\ensuremath{\sigma}\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ behavior in the nonmetallic regime. For intermediate disorder at 1/4 electronic filling, a metal-to-insulator transition is predicted to take place at a critical $U/B\ensuremath{\approx}0.75$ ($U$ being the Hubbard interaction strength and $B$ the electronic band width). Our numerical results show that the formation of magnetic moments is essential to the suppression of the density of states at the Fermi level and therefore essential to the metal-insulator transition. At weaker disorder a small lessening of the density of states at the Fermi level occurs but screening suppresses the spatial disorder and with increasing interactions no metal-insulator transition is found.

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