A Critical Analysis of the Mean-Field Approximation for the Calculation of the Magnetic Moment in the Friedel-Anderson Impurity Model

TL;DR

This paper critically examines the mean-field approximation for calculating magnetic moments in the Friedel-Anderson impurity model, revealing its unreliability and proposing an optimized solution that significantly alters magnetic predictions.

Contribution

The authors introduce an optimized solution in rotated Hilbert space that improves upon mean-field results for magnetic moments in the Friedel-Anderson model.

Findings

Mean-field calculations are unreliable for magnetic moments.

Optimized solutions require nearly twice the Coulomb U to induce magnetism.

Most existing magnetic impurity calculations need reexamination.

Abstract

It is shown that the calculation of the magnetic moment of a Friedel-Anderson impurity in mean-field theory is unreliable. A class of approximate solutions, which contains the mean-field solution as an element, is expressed in rotated Hilbert space and optimized. The optimal state has considerably lower energy than the mean field solution and requires almost twice the Coulomb exchange U to become magnetic. Since most moment calculations of magnetic impurities, for example the spin-density-functional theory, use the mean-field approximation the resulting magnetic moments have to be critically reexamened.(After publication the reference can be found at "http://physics.usc.edu/~bergmann/") PACS: 75.20.Hr