Proper weak-coupling approach to the periodic s-d(f) exchange model

TL;DR

This paper introduces a projection-operator method for the periodic s-d(f) exchange model, providing a reliable weak-coupling approach that captures quantum effects and correctly incorporates known limiting cases.

Contribution

It proposes a novel weak-coupling method based on projection operators, improving upon existing approximations for the s-d(f) exchange model.

Findings

Results include insights beyond perturbation theory.

Method accurately reproduces known limiting cases.

Provides guidelines for more effective modeling of the exchange interaction.

Abstract

The periodic s-d(f) exchange model is characterized by a wide variety of interesting applications, a simple mathematical structure and a limited number of reliable approximations which take care of the quantum nature of the participating spins. We suggest the use of a projection-operator method for getting information perturbationally, which are not accessible via diagrammatic approaches. In this paper we present in particular results beyond perturbation theory, which are obtained such that almost all exactly known limiting cases are incorporated correctly. We discuss a variety of possible methods and evaluate their consequences for one-particle properties. These considerations serve as a guideline for a more effective approach to the model.