A Compact Approximate Solution to the Kondo Problem

TL;DR

This paper presents a simplified approximate groundstate solution to the Kondo problem, capturing key energy features and the Kondo temperature with a compact four-state model.

Contribution

It introduces a novel four Slater state approximation that efficiently models the Kondo groundstate and calculates energies for both ferromagnetic and antiferromagnetic couplings.

Findings

Groundstate energy and excitation energy calculated numerically.

Singlet-triplet excitation energy proportional to exp[-1/2Jg].

Close approximation to the Kondo temperature k_BT_K.

Abstract

A compact approximate groundstate of the Kondo problem is introduced. It consists of four Slater states. The spin up and down states of the localized d-impurity are paired with two localized s-electron states of opposite spin. All the remaining s-electron states are rearranged forming two new optimal orthonormal bases. Through a rotation in Hilbert space the two localized states (and the rest of the bases) are optimized by minimizing the energy expectation value. The ground-state energy E and the singlet-triplet excitation energy dE are calculated numerically. Although the two energies can differ by a factor of 1000, they are obtained simultaneously. The singlet-triplet excitation energy dE is proportional to exp[-1/2Jg] and quite close to the Kondo temperature k_BT_K. The cases for anti-ferromagnetic (J>0) and ferromagnetic (J<0) coupling are investigated.