Competition between Coqblin-Schrieffer and local exchange interactions in Kondo systems by the perturbative renormalization group

Abstract

A model which accounts for the competition between hybridization and local exchange (LE) interactions in anomalous Ce systems is proposed. In this model a localized magnetic moment ${j}_{f}=5/2$ has an antiferromagnetic Coqblin-Schrieffer (CS) coupling with $l=3$ conduction electrons partial waves, due to hybridization, and a contact coupling with $l=0$ partial waves due to the LE interaction. The last term breaks the $\mathrm{SU}(N)$ symmetry of the CS model. Using the perturbative renormalization group, we show that the $\mathrm{SU}(N)$ ground state of the CS model remains the ground state even in the presence of a LE interaction stronger than the CS coupling. We discuss the effect of the LE on the Kondo temperature. Moreover, when the LE coupling reaches a critical value the system has a non-Fermi-liquid non-$\mathrm{SU}(N)$ ground state, and when it is stronger than the critical value the system falls into an undercompensated Kondo state.