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arXiv:cond-mat/9609057 · Nuclear Physics B

On two channel flavor anisotropic and one channel compactified Kondo models

Jinwu Ye

Published Feb 1, 1998• 6 citations
arXivHTMLPDF

Abstract

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 π/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 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.

DOI
10.1016/s0550-3213(97)80485-3

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Using the numerical renormalization group method, we study a generalized two-channel Kondo model where the impurity has a quadrupole moment (pseudospin) and a magnetic moment (flavor). This model may be of relevance to the Ce ions in CeB6{\mathrm{CeB}}_{6}CeB6​ and the Cu ions in cuprate superconductors. We find that the nontrivial fixed point of the two-channel Kondo model is unstable against flavor exchange coupling. The system flows to a non-Fermi-liquid fixed line. In the presence of a double tensor interaction, which breaks particle-hole symmetry, the system flows to a Fermi-liquid fixed line.
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Recent experiments by Potok et al. have demonstrated a remarkable tunability between a single-channel Fermi-liquid fixed point and a two-channel non-Fermi-liquid fixed point. Motivated by this we study the nonequilibrium dynamics due to a sudden quench of the parameters of a Hamiltonian from a single-channel to a two-channel anisotropic Kondo system. We find a distinct difference between the long-time behavior of local quantities related to the impurity spin as compared to that of bulk quantities related to the total (conduction electrons plus impurity) spin of the system. In particular, the local impurity spin and the local spin susceptibility are found to equilibrate but in a very slow power-law fashion which is peculiar to the non-Fermi-liquid properties of the Hamiltonian. In contrast, we find a lack of equilibration in the two-particle expectation values related to the total spin of the system.