Effective medium super-cell approximation for interacting disordered systems: analternative real-space derivation of generalized dynamical cluster approximation

Abstract

We develop a generalized real-space effective medium super-cell approximation (EMSCA)method to treat the electronic states of interacting disordered systems. This method isgeneral and allows randomness both in the on-site energies and in the hopping integrals.For a non-interacting disordered system, in the special case of randomness in theon-site energies, this method is equivalent to the non-local coherent potentialapproximation (NLCPA) derived previously. Also, for an interacting system the EMSCAmethod leads to the real-space derivation of the generalized dynamical clusterapproximation (DCA) for a general lattice structure. We found that the originalDCA and the NLCPA are two simple cases of this technique, so the EMSCAis equivalent to the generalized DCA where there is included interaction andrandomness in the on-site energies and in the hopping integrals. All of the equations ofthis formalism are derived by using the effective medium theory in real space.