Coherent Cluster Theory for Static and Dynamic Disordered Systems on Bethe Lattices

Abstract

A new systematic cluster theory beyond the single-site coherent potential approximation is presented for averaged one-particle Green’s functions. The formalism is developed in augmented-space and illustrated for site-diagonal disorder. The theoretical feature is to treat overlapping clusters exactly by employing a kind of the matrix continued fraction. The resulting Green’s functions are analytic, translationally invariant, and predict proper limiting behaviors at weak or strong scattering and high or low concentrations. Model calculations for a static disordered chain are shown to compare well with the essentially exact calculation.