Strong coupling in the Kondo problem in the low-temperature region

TL;DR

This paper investigates the magnetic field dependence of a localized electron's spin in the Kondo problem at low temperatures, revealing inflection points and corrections in different magnetic field regimes.

Contribution

It provides a detailed analysis of the spin behavior and energy splitting in the Kondo problem under varying magnetic fields at low temperatures.

Findings

Inflection point at  H   0.5 T_c

Correction to spin proportional to (T_c/ H)^2 for  H \u226b T_c

Magnetic field causes splitting of degenerate impurity states at zero field

Abstract

The magnetic field dependence of the average spin of a localized electron coupled to conduction electrons with an antiferromagnetic exchange interaction is found for the ground state. In the magnetic field range $\mu H\sim 0.5 T_c$ ($T_c$ is the Kondo temperature) there is an inflection point, and in the strong magnetic field range $\mu H\gg T_c$, the correction to the average spin is proportional to $(T_c/\mu H)^2$. In zero magnetic field, the interaction with conduction electrons also leads to the splitting of doubly degenerate spin impurity states.