Diagrammatic method for investigating universal behavior of impurity systems

TL;DR

This paper introduces a diagrammatic approach using skeleton diagrams to analyze the universal behavior of magnetic impurity systems, deriving energy scales and assessing approximation methods.

Contribution

It presents a novel diagrammatic method that identifies a minimal set of skeleton diagrams for exact scaling and evaluates the non-crossing approximation's effectiveness.

Findings

The method derives energy scales from skeleton diagrams.

The non-crossing approximation describes crossover phenomena.

The universal Wilson-number is calculated within this framework.

Abstract

The universal behavior of magnetic impurities in a metal is proved with the help of skeleton diagrams. The energy scales are derived from the structure of the skeleton diagrams. A minimal set of skeleton diagrams is sorted out that scales exactly. For example, the non-crossing approximation for the Anderson impurity model can describe the crossover phenomenon. The universal Wilson-number is calculated within the non-crossing approximation. The method allows for an assessment of various approximations for impurity Hamiltonians.