Non-crossing approximation

In this section, we survey some of the most important applications of the NCA to the multichannel Kondo model. We shall first discuss application of the NCA to the SU(M) x SU(N _I = N _c = N) Anderson model for which the results are rigorous as N → ∞ with γ = M/N fixed. Despite the large-N character of the theory, the physical properties computed for finite N, M are found to be in good agreement with exact results for most properties. Next, we shall discuss an application to a simple three-configuration model for a Ce³⁺ ion which illustrates single-, two- and threechannel Kondo physics in appropriate regimes. An important physical result which emerges from this analysis is that the sign of the low-temperature thermopower is a diagnostic for the emergence of the two-channel ground state as required by the dynamic selection rule 5 of section 2.2.4. Finally, we shall apply the NCA to a model for the U⁴⁺ ion which includes both ground-state and excited-state crystal-field 129levels. These results show how the two-channel physics can emerge at low temperatures even with significant overlap between crystal-field states owing to conduction-electron damping.