Mott-Hubbard Transition and Anderson Localization: Generalized Dynamical Mean-Field Theory Approach

Density of states, dynamic (optical) conductivity and phase diagram of strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT+\Sigma approximation). Strong correlations are accounted by DMFT, while disorder is taken into account via the appropriate generalization of self-consistent theory of localization. The DMFT effective single impurity problem is solved by numerical renormalization group (NRG) and we consider the three-dimensional system with semi-elliptic density of states. Correlated metal, Mott insulator and correlated Anderson insulator phases are identified via the evolution of density of states and dynamic conductivity, demonstrating both Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of complete zero-temperature phase diagram of Anderson-Hubbard model. Rather unusual is the possibility of disorder induced Mott insulator to metal transition.