Statistics of local density of states in the Falicov-Kimball model with local disorder

Statistics of the local density of states in the two-dimensional Falicov-Kimball model with local disorder is studied by employing the statistical dynamical mean-field theory. Within the theory, the local density of states and its distributions are calculated through stochastic self-consistent equations. The most probable value of the local density of states is used to monitor the metal-insulator transition driven by correlation and disorder. Nonvanishing of the most probable value of the local density of states at the Fermi energy indicates the existence of extended states in the two-dimensional disordered interacting system. It is also found that the most probable value of the local density of states exhibits a discontinuity when the system crosses from extended states to the Anderson localization. A phase diagram is also presented.