Self-Consistent Strong-Coupling-Perturbation Theory for the Anderson Model, Based on Wicks Theorem

TL;DR

This paper develops a self-consistent strong-coupling perturbation theory for the Anderson model using Wick's theorem, enabling detailed analysis of the $f$-electron spectrum without auxiliary particles.

Contribution

It introduces a novel self-consistent diagrammatic approach for the Anderson model that avoids auxiliary particles and extends to lattice models within the local approximation.

Findings

The $f$-electron spectrum is computed using the new method.

Comparison shows agreement with the Non-Crossing Approximation.

Extension to lattice models is proposed.

Abstract

A strong-coupling-perturbation theory around the Atomic Limit of the Anderson model with large $U$ for a localized $f$-orbital coupled to a conduction-electron band is presented. Although an auxiliary-particle representation is {\em not} used, application of the canonical Wick's theorem is possible and yields an expansion in the hybridization $V$ via dressed skeleton-Feynman diagrams. The Self-Consistent T-Approximation is constructed as a $\Phi$-derivable approximation. From a numerical solution of self-consistency equations the $f$-electron-excitation spectrum is investigated. Comparison to the Non-Crossing Approximation is made in virtue of exact formal relations and numerical results. An extension of this Feynman-diagram approach to the Anderson-lattice model is indicated, and application within the Local-Approximation scheme (limit of infinite spatial dimension) is given.