Diagrammatic theory for twofold degenerate Anderson impurity model

TL;DR

This paper develops a diagrammatic theoretical framework to analyze the twofold degenerate Anderson impurity model, incorporating strong electronic correlations and providing a basis for calculating impurity properties.

Contribution

It introduces a novel diagrammatic approach for the twofold degenerate Anderson impurity model, including eigenfunction analysis and a Dyson equation for the impurity's Green's function.

Findings

Derived the eigenfunctions and eigenvalues of local impurity states

Formulated the Dyson equation for the renormalized propagator

Developed a diagrammatic approximation for correlation functions

Abstract

The twofold degenerate Anderson impurity model [1-4] is investigated and the strong electronic correlations of d-electrons of impurity ion are taken into account by elaborating suitable diagram technique. We discuss the properties of the Slater-Kanamori model [2-4] of d-impurity electrons. After finding the eigenfunctions and eigenvalues of all 16 local states, we determine the local one-particle propagator. Then we construct the perturbation theory around the atomic limit of the impurity ion and obtain the Dyson type equation for the renormalized one-particle propagator. Diagrammatic theory has been developed and correlation function determined. Special diagrammatic approximation was discussed and summation of diagram has been considered.