Overscreened single-channel Kondo problem.

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-ansatz 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-\textonehalf{} electrons with $k(j)=2\frac{j(j+1)(2j+1)}{3}$. 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 the $k(j)$-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.