We reformulate the two-channel Kondo model to explicitly remove the unscattered charge degrees of freedom. This procedure permits us to move the non-Fermi-liquid fixed point to infinite coupling where we can apply a perturbative strong-coupling expansion. The fixed-point Hamiltonian involves a three-body Majorana zero mode whose scattering effects give rise to marginal self-energies. The compactified model is the N=3 member of a family of O(N) Kondo models that can be solved by semiclassical methods in the large N limit. For odd N, fermionic ``kink'' fluctuations about the N=\ensuremath{\infty} mean-field theory generate a fermionic N-body bound state which asymptotically decouples at low energies. For N=3, our semiclassical methods fully recover the non-Fermi-liquid physics of the original two-channel model. Using the same methods, we find that the corresponding O(3) Kondo lattice model develops a spin-gap and a gapless band of coherently propagating three-body bound states. Its strong-coupling limit offers a rather interesting realization of a marginal Fermi liquid.
The bosonization of the S=1/2 anisotropic two-channel Kondo model is shown to yield two equivalent representations of the original problem. In a straight-forward extension of the Emery-Kivelson approach, the interacting resonant level model previously derived by the Anderson-Yuval technique is obtained. In addition, however, a compactified ``(\ensuremath{\sigma},\ensuremath{\tau})'' description is also found. The strong coupling fixed point of the (\ensuremath{\sigma},\ensuremath{\tau}) model was originally postulated to be related to the intermediate coupling fixed point of the two-channel Kondo model. The equivalence of the \ensuremath{\sigma},\ensuremath{\tau} model to the two-channel Kondo model is formally established. A summary of what one may learn from a simple study of these different representations is also given.
We solve the multichannel Kondo model with channel anisotropy using the Bethe ansatz method. The model generates energy scales, characterizing the neighborhoods of the various infrared fixed points, reflecting the structure of the symmetry breaking in the channel sector. The nature of these fixed points also depends on the magnitude of the impurity spin
S. We present a detailed discussion for the two channel case and point out some possible non-Fermi-liquid behavior.
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-
21 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-
21 local moment is shown to exist for large ${J}_{z}⪢\ensuremath{\mid}{J}_{\ensuremath{\perp}}\ensuremath{\mid}>0$ and arbitrary
k and
s obeying $\ensuremath{\mid}k\ensuremath{-}2s\ensuremath{\mid}>1$. Here,
Jz is the longitudinal spin-exchange coupling, ${J}_{\ensuremath{\perp}}$ 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>1∕2 and arbitrary
k. Depending on the sign of ${J}_{z}^{2}\ensuremath{-}{J}_{\ensuremath{\perp}}^{2}$ and the parity of
2s, the system flows either to a conventional Fermi liquid with no residual degeneracy or to a
k-channel, spin-
21 Kondo effect or to a line of ferromagneticlike fixed points with a residual isospin-
21 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.
We reinvestigate the two channel flavor anisotropic model (2CFAK) and one channel compacitified Kondo model (1CCK). For these two models, all the possible fixed points and their symmetries are identified; the finite size spectra, the electron conductivity and pairing susceptibility are calculated. It is shown that the only non-fermi liquid (NFL) fixed point of the 2CFAK is the NFL of the two channel Kondo model (2CK) with the symmetry
O(3)×O(5). Any flavor anisotropies between the two channels drive the system to the fermi-liquid (FL) fixed point with the symmetry
O(4)×O(4) where one of the two channels suffers the phase shift π/2 and the other remains free. The NFL fixed point of the 1CCK has the symmetry
O(3)×O(1) and has the same thermodynamics as the NFL fixed point of the 2CK. However, in contrast to the 2CK, its conductivity shows
T2 behavior and there is no pairing susceptibility divergence. Any anisotropies between the spin and isospin sectors drive the system to the FL fixed point with the symmetry O(4) where the electrons suffer the phase shift π/2. The connection and differences between the two models are explicitly demonstrated. The recent conjectures and claims on the NFL behaviors of the two models are commented.
We have performed full-scale numerical-renormalization-group calculations on the anisotropic, two-channel, impurity spin s=1/2 Kondo Hamiltonian. To allow for anisotropy we have worked in a basis of total axial charge
ja and
jb (a and b index the channels) as well as total
Sz. In the isotropic limit, our results agree well with the previous work of Cragg, Lloyd, and Nozieres. The most important results are (1) confirmation of the approach to a nontrivial fixed point from weak coupling, (2) the stability of the fixed point against exchange anisotropy, and (3) the destabilization of the fixed point by the application of a magnetic field or the lifting of exchange symmetry between two channels. We find the crossover temperature scales with the square of the exchange splitting.