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

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