Beyond the Nca: New Results for the Spectral Properties of the Anderson Model

TL;DR

This paper introduces a self-consistent approximation beyond NCA for the Anderson Model, improving spectral and Fermi-liquid properties, with results closely matching exact solutions and sum rules.

Contribution

It presents a new resummation technique including all contributions up to order 1/N^2, enhancing the spectral and Fermi-liquid descriptions of the Anderson Model.

Findings

Improved spectral resonance location and temperature dependence matching Friedel's sum rule.

Static magnetic susceptibility aligns with Bethe-Ansatz solutions.

Qualitative improvements over NCA in maintaining Fermi-Liquid relations.

Abstract

In the framework of direct perturbation theory a fully self-consistent approximation beyond the well known NCA will be presented for the Anderson Model. The resummation of a class of skeleton diagrams up to infinite order in $V$ includes all contribution up to the order $O(1/N^2)$ ( $N$ = degeneracy of the magnetic state). Qualitative improvements in maintaining local Fermi-Liquid relations and one-particle spectral properties in comparison to the well known NCA will be reported. The location and temperature dependence of the AS-resonance for the case $N=2$ is found to be rather close to the chemical potential in excellent agreement with Friedel's sum rule; the static magnetic susceptibility exhibits the same $N$-dependence as the exact {\em Bethe-Ansatz} solution.