Phase diagram of the anisotropic multichannel Kondo Hamiltonian revisited

Abstract

The phase diagram of the multichannel Kondo Hamiltonian with an XXZ spin-exchange anisotropy is revisited, revealing a far richer fixed-point structure than previously appreciated. For a spin-1/2 impurity and k > 2 conduction-electron channels, a second ferromagnetic-like domain is found deep in the antiferromagnetic regime. The new domain extends above a (typically large) critical longitudinal coupling J_z^{\ast} > 0, and is separated from the antiferromagnetic domain by a second Kosterliz-Thouless line. A similar line of stable ferromagnetic-like fixed points with a residual isospin-1/2 local moment is shown to exist for large J_z >> |J_{\perp}| > 0 and arbitrary k and s obeying |k - 2s| > 1. Here J_z is the longitudinal spin-exchange coupling, J_{\perp} is the transverse coupling, and s is the impurity spin. Near the free-impurity fixed-point, spin-exchange anisotropy is a relevant perturbation for s > 1/2 and arbitrary k. Depending on the sign of J_z^2 - J_{\perp}^2 and the parity of 2s, the system flows either to a conventional Fermi liquid with no residual degeneracy, or to a k-channel, spin-1/2 Kondo effect, or to a line of ferromagnetic-like fixed points with a residual isospin-1/2 local moment. These results are obtained through a combination of perturbative renormalization-group techniques, Abelian bosonization, a strong-coupling expansion in 1/J_z, and explicit numerical renormalization-group calculations.