Systematic and causal corrections to the coherent potential approximation

The dynamical cluster approximation ~DCA! is modified to include disorder. The DCA incorporates nonlocal corrections to local approximations such as the coherent potential approximation ~CPA! by mapping the lattice problem with disorder, and in the thermodynamic limit, to a self-consistently embedded finite-sized cluster problem. It satisfies all of the characteristics of a successful cluster approximation. It is causal, preserves the point-group and translational symmetry of the original lattice, recovers the CPA when the cluster size equals one, and becomes exact as Nc→` . We use the DCA to study the Anderson model with binary diagonal disorder. It restores sharp features and band tailing in the density-of-states, which reflect correlations in the local environment of each site. While the DCA does not describe the localization transition, it does describe precursor effects of localization.