Density of States in the Magnetic Ground State of the Friedel-Anderson Impurity

TL;DR

This paper uses the FAIR method to analyze the magnetic ground state of the Friedel-Anderson impurity, revealing broader d-resonances and explaining the increased critical Coulomb interaction compared to mean field theory.

Contribution

The paper introduces a detailed calculation of the density of states in the magnetic ground state using the FAIR approach, providing new insights into resonance broadening.

Findings

Resonance width is about twice the mean field prediction.

Resonance broadening reduces the density of states by a factor of two.

Critical Coulomb interaction is twice the mean field estimate.

Abstract

By applying a magnetic field whose Zeeman energy exceeds the Kondo energy by an order of magnitude the ground state of the Friedel-Anderson impurity is a magnetic state. In recent years the author introduced the Friedel Artificially Inserted Resonance (FAIR) method to investigate impurity properties. Within this FAIR approach the magnetic ground state is derived. Its full excitation spectrum and the composition of the excitations is calculated and numerically evaluated. From the excitation spectrum the electron density of states is calculated. Majority and minority d-resonances are obtained. The width of the resonances is about twice as wide as the mean field theory predicts. This broadening is due to the fact that any change of the occupation of the d-state in one spin band changes the eigenstates in the opposite spin band and causes transitions in both spin bands. This broadening reduces the height of the resonance curve and therefore the density of states by a factor of two. This yields an intuitive understanding for a previous result of the FAIR approach that the critical value of the Coulomb interaction for the formation of a magnetic moment is twice as large as the mean field theory predicts.