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Transition from a strong-coupling fixed point to an intermediate-coupling fixed point in a single-channel SU(N) Kondo model: role of the filling and two-stage screening

We study an extended SU(N) single-impurity Kondo model in which the impurity spin is described by a combination of Abrikosov fermions and Schwinger bosons. Our aim is to describe both the quasiparticle-like 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 identify the strong coupling fixed point of the model and study its stability within second order perturbation theory. 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 as soon as the amount of Abrikosov fermions reaches a critical value. In the stability region, the partially screened, dressed impurity at site 0 repels the conduction electrons on adjacent sites. In the instability region, the impurity tends to attract $(N-1)$ conduction electrons to the neighboring sites, giving rise to a two-stage Kondo effect with additional screening.This result opens the route to the existence of an intermediate coupling fixed point, characterized by non-Fermi liquid behavior.