Overscreened Single Channel Kondo Problem

TL;DR

This paper analyzes the overscreened single channel Kondo problem, revealing that its spin dynamics match a multi-channel Kondo model with specific channel count, leading to non-Fermi liquid behavior for certain parameters.

Contribution

It demonstrates that the spin sector dynamics are equivalent to a multi-channel Kondo model with a specific number of channels, contrasting previous conjectures, and uses conformal field theory to analyze the spectrum.

Findings

System exhibits non-Fermi liquid behavior when 2S < k(j).

Finite-size spectrum differs from standard models due to additional sectors.

Conformal field theory techniques reveal operator content differences.

Abstract

We consider the single channel Kondo problem with the Kondo coupling between a spin $S$ impurity and conduction electrons with spin $j$. These problems arise as multicritical points in the parameter spaces of two- and higher-level tunneling systems, and some impurity models of heavy fermion compounds. In contrast to the previous Bethe-anstaz conjectures, it turns out that the dynamics of the spin sector is the same as that of a spin $S$ impurity coupled to $k(j)$ channels of spin $1/2$ electrons with $k(j) = 2j(j+1)(2j+1)/3$. As a result, for $2S < k(j)$, the system shows non-Fermi liquid behavior with the same exponents for the thermodynamic quantities as those of $k(j)$ channel Kondo problem. However, both the finite-size spectrum and the operator content are different due to the presence of the other sectors and can be obtained by conformal field theory techniques.