The Friedel-Anderson and Kondo Impurity Problem for Arbitrary s-Band Density of States and Exchange Interaction

TL;DR

This paper extends Wilson's method for the Kondo problem to arbitrary s-band densities of states, enabling more accurate impurity interaction modeling with minimal error, demonstrated through numerical calculations.

Contribution

It adapts Wilson states to handle arbitrary s-band densities, improving the modeling of impurity interactions beyond constant density assumptions.

Findings

Wilson states effectively model arbitrary s-bands.

Minor errors introduced by the approximation.

Numerical calculation of Kondo excitation energy for complex bands.

Abstract

In his renormalization paper of the Kondo effect Wilson replaced the full band of s-electrons by a small number of ''Wilson states''. He started from a rather artificial symmetric band with constant density of states and constant interaction with the impurity. It is shown in the present paper that with a minor modification the Wilson states are optimally suited to treat the interaction of an impurity with an arbitrary s-band. Each Wilson state represents electrons of a whole energy range. It carries the interaction of all these electrons with the impurity. All the other electron states in this energy range have zero interaction with the impurity and are neglected in the calculation. The resulting error is minor. As an example the singlet-triplet excitation energy of a Kondo impurity is numerically calculated for a tight-binding band with a strongly energy dependent density of states.