The embedding problem in ordered and disordered systems

Abstract

General aspects of the embedding problem are critically reconsidered. It is shown that two different approaches are possible, the perturbed-host-system approach, and the self-energy or perturbed-cluster approach; the fields of application of the corresponding computational schemes are largely complementary. In both cases, detailed knowledge is required of the Green function of the extended host system, in the local region where the defect has to be created. This aspect of the problem is examined in some detail in the present work, particular attention being given to a case where the host system is characterized by compositional disorder. As an example, solutions to the embedding problem are given for an ideal one-dimensional alloy and are subsequently discussed.