On two channel flavor anisotropic and one channel compactified Kondo models

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 $O(3) \times O(5)$. Any flavor anisotropies between the two channels drive the system to the fermi-liquid (FL) fixed point with the symmetry $O(4) \times O(4)$ where one of the two channels suffers the phase shift \pi/2 and the other remains free. The NFL fixed point of the 1CCK has the symmetry $O(3) \times O(1)$ and has the same thermodynamics as the NFL fixed point of the 2CK. However, in contrast to the 2CK, its conductivity shows $T^{2}$ 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 \pi/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.