Wick's Theorem and a New Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems

TL;DR

This paper introduces a novel perturbation expansion for strongly correlated electron systems based on Wick's theorem, accurately incorporating local correlations and recovering key energy scales, with extensions to lattice models.

Contribution

It presents a new perturbation theory around the atomic limit using Feynman diagrams without auxiliary particles, applicable to Anderson and lattice models.

Findings

Successfully recovers the Kondo energy scale.

Analytically treats an infinite-order ladder resummation.

Extends to Anderson-lattice models via cumulant expansion.

Abstract

A new type of perturbation expansion in the mixing $V$ of localized orbitals with a conduction-electron band in the $U\to\infty$ Anderson model is presented. It is built on Feynman diagrams obeying standard rules. The local correlations of the unperturbed system (the atomic limit) are included exactly, no auxiliary particles are introduced. As a test, an infinite-order ladder-type resummation is analytically treated in the Kondo regime, recovering the correct energy scale. An extension to the Anderson-lattice model is obtained via an effective-site approximation through a cumulant expansion in $V$ on the lattice. Relation to treatments in infinite spatial dimensions are indicated.