Perturbational Approach to the Anderson Model: New Results from a Post-Nca Treatment

TL;DR

This paper introduces an advanced perturbative method for the Anderson-impurity model that surpasses the non-crossing approximation by including infinite-order skeleton diagrams, leading to improved spectral and Fermi-liquid property predictions.

Contribution

It develops a post-NCA approach incorporating infinite-order crossing diagrams and all $1/N^2$ contributions, providing more accurate results for the Anderson model.

Findings

Improved threshold behavior of local propagators.

Qualitative enhancement of spectral properties.

Progress in achieving local Fermi-liquid characteristics.

Abstract

We present selected results from combined analytical and numerical studies of the Anderson-impurity model within the framework of infinite order perturbation theory with respect to the hybridization. Our approximation goes considerably beyond the well known non\-cross\-ing approximation (NCA): The re-summations include skeleton diagrams up to infinite order of the cross\-ing variety, including all $1/N^2$ contributions ($N =$ degeneracy of the magnetic state). We demonstrate, in a comparison with NCA theory, changes in the threshold behaviour of local propagators, a qualitative improvement of spectral properties and a clear progress in attaining local Fermi-liquid properties. Further applications of the post-NCA theory are pointed out.