A Compact Treatment of the Friedel-Anderson and the Kondo Impurity Using the FAIR Method

TL;DR

The paper introduces the FAIR method, a compact approach that effectively calculates spatial properties of the Kondo ground state, including the elusive Kondo cloud, with results aligning well with established theories.

Contribution

It presents the FAIR method as a simple, accurate tool for analyzing the spatial distribution of electrons in Kondo and Friedel-Anderson impurities, including the first calculation of the Kondo cloud.

Findings

FAIR method yields accurate spatial electron densities.

Excellent agreement with N-approximation and NRG results.

First calculation of the electronic polarization in the Kondo cloud.

Abstract

Although the Kondo effect and the Kondo ground state of a magnetic impurity have been investigated for more than forty years it was until recently difficult if not impossible to calculate spatial properties of the ground state. In particular the calculation of the spatial distribution of the so-called Kondo cloud or even its existence have been elusive. In recent years a new method has been introduced to investigate the properties of magnetic impurities, the FAIR method, where the abbreviation stands for Friedel Artificially Inserted Resonance. The FAIR solution of the Friedel-Anderson and the Kondo impurity problems consists of only eight or four Slater states. Because of its compactness the spatial electron density and polarization can be easily calculated. In this article a short review of the method is given. A comparison with results from the large N-approximation, the Numerical Renormalization Group theory and other methods shows excellent agreement. The FAIR solution yields (for the first time) the electronic polarization in the Kondo cloud.