Strong-coupling fixed point instability in a single-channel SU(N) Kondo model

We study a generalized SU(N) single-impurity Kondo model in which the impurity spin is described by a combination of q Abrikosov fermions and (2S-1) Schwinger bosons. Our aim is to describe both the quasiparticlelike excitations and the locally critical modes observed in various physical situations, including non-Fermi-liquid behavior in heavy-fermion systems in the vicinity of a quantum critical point. We carry out an analysis of the strong-coupling fixed point, from which an effective Hamiltonian is derived containing both a charge interaction and a spin coupling between n_d nearest-neighbor electrons and the screened impurity. The effective charge interaction is already present in the case of a purely fermionic impurity and it changes from repulsive to attractive at q=N/2, due to the [Formula Presented] symmetry. The sign of the effective spin coupling determines the stability of the strong-coupling fixed point. Already in the single-channel case and in contrast with either the pure bosonic or the pure fermionic case, the strong-coupling fixed point is unstable against the conduction electron kinetic term in the large-N limit as soon as q>N/2. The origin of this change of regime is directly related to the sign of the effective charge interaction.