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

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.

19 pages in REVTEX 2.0, 2 tables, 3 figures. Submitted to Phys. Rev. B. The reference .bbl file is appended at the end. 3 figures in postscript files can be obtained at [email protected]. The filename is gan.figures.tar.z and it's compressed. You can uncompress it by using commands: "uncompress gan.figures.tar.z" and "tar xvf gan.figures.tar". UBC