Phase diagram of the anisotropic multichannel Kondo Hamiltonian revisited

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 ferromagneticlike domain is found deep inside the antiferromagnetic regime. The new domain extends above a (typically large) critical longitudinal coupling Jz*>0 and is separated from the antiferromagnetic domain by a second Kosterlitz-Thouless line. A similar line of stable ferromagneticlike fixed points with a residual isospin-1/2 local moment is shown to exist for large Jz⪢J_⊥>0 and arbitrary k and s obeying k-2s>1. Here, Jz is the longitudinal spin-exchange coupling, J_⊥ is the transverse coupling, and s is the impurity spin. Near the free-impurity fixed point, spin-exchange anisotropy generates a highly relevant term for $s>1∕2$ and arbitrary k. Depending on the sign of Jz²-J_⊥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 ferromagneticlike 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∕Jz, and explicit numerical renormalization-group calculations.