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 J_z^*>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 J_z⪢∣J_⊥∣>0 and arbitrary k and s obeying ∣k−2s∣>1. Here, J_z 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 J_z²−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∕J_z, and explicit numerical renormalization-group calculations.