Phase diagram of the anisotropic multichannel Kondo Hamiltonian revisited
Avraham Schiller and Lorenzo De Leo

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-$\frac{1}{2}$ impurity and $k &gt 2$ conduction-electron channels, a second ferromagnetic-like domain is found deep inside the antiferromagnetic regime. The new domain extends above a (typically large) critical longitudinal coupling $J_z^{\ast} &gt 0$, and is separated from the antiferromagnetic domain by a second Kosterlitz-Thouless line. A similar line of stable ferromagnetic-like fixed points with a residual isospin-$\frac{1}{2}$ local moment is shown to exist for large $J_z \gg |J_{\perp}| &gt 0$ and arbitrary $k$ and $s$ obeying $|k - 2s| &gt 1$. 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 generates a highly relevant term for $s &gt 1/2$ 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-$\frac{1}{2}$ Kondo effect, or to a line of ferromagnetic-like fixed points with a residual isospin-$\frac{1}{2}$ 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.

© 2008 The American Physical Society.