A Compact Approximate Solution to the Friedel-Anderson Impuriy Problem

TL;DR

This paper introduces a compact approximate ground state solution for the Anderson-Friedel impurity problem, simplifying the complex many-body problem to optimize only two localized states, and achieves results close to numerical solutions.

Contribution

It presents a new, simplified approximate ground state that requires only the optimization of two localized states, providing a more efficient solution to the impurity problem.

Findings

Ground state energy is significantly lower than mean field solutions.

Results agree well with extensive numerical methods by Gunnarsson and Schoenhammer.

The approach simplifies the complex impurity problem with minimal parameters.

Abstract

An approximate groundstate of the Anderson-Friedel impurity problem is presented in a very compact form. It requires solely the optimization of two localized electron states and consists of four Slater states (Slater determinants). The resulting singlet ground state energy lies far below the Anderson mean field solution and agrees well with the numerical results by Gunnarsson and Schoenhammer, who used an extensive 1/N_{f}-expansion for a spin 1/2 impurity with double occupancy of the impurity level. PACS: 85.20.Hr, 72.15.Rn