On Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems: A New Approach Based on Wick's Theorem

TL;DR

This paper introduces a novel perturbation method for strongly correlated electron systems using Wick's theorem, enabling analytical reproduction of key features like the Kondo resonance without auxiliary particles.

Contribution

It develops a new perturbational approach based on Wick's theorem for the Anderson model at infinite U, incorporating local correlations exactly through a two-particle vertex.

Findings

Reproduces the small energy scale of the Kondo resonance analytically.

Provides a perturbation expansion of Green's functions using standard Feynman diagrams.

Eliminates the need for auxiliary particles in the theoretical framework.

Abstract

A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect to the hybridization $V$ built on Feynman diagrams obeying standard rules is possible. The local correlations of the unperturbed system (the atomic limit) are included exactly through a two-particle vertex. No auxiliary particles are introduced into the theory. As an example and test the small energy scale and many-body resonance of the Kondo problem are reproduced analytically.