Kondo Crossover In The Self-Consistent One-Loop Approximation"

TL;DR

This paper extends the $1/N$ expansion technique to calculate the magnetization in the $SU(N)$ Kondo model, providing an analytically asymptotically exact universal magnetization curve across different magnetic field regimes.

Contribution

It introduces a self-consistent one-loop approximation for the $SU(N)$ Kondo model, improving understanding of the crossover behavior and verifying the non-singular nature of the $1/N$ parameter.

Findings

Universal magnetization curve $M(h/T_{K})$ is asymptotically exact at both limits.

Curves cross continuously from weak to strong coupling, overestimating the crossover curvature.

Magnetic Wilson crossover numbers are explicitly calculated.

Abstract

The free energy and magnetization for the general $SU(N)$ one impurity Kondo model in the magnetic field, $h$, are calculated by extending the previous $1/N$ expansion technique: the saddle point is determined self-consistently to the $1/N$ order. The obtained universal field dependent magnetization $M(h/T_{K})$ by this simple method is shown analytically to be asymptotically exact at both $h \ll T_{K}$ and $h \gg T_{K}$ limits. For general ''$f$-electron'' fillings, except half filling, the $M(h/T_{K})$ curves cross continuously from weak to strong coupling limit, but overestimate the curvature in the crossover region for moderate $N$. The magnetic Wilson crossover numbers are calculated for amusement. Our results explicitly verify that the $1/N$ parameter is non-singular under the adiabatic continuation.