A Compact Treatment of the Friedel-Anderson and the Kondo Impurity Using the FAIR Method (Friedel Artificially Inserted Resonance)

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.