The single-impurity Kondo problem can be mapped onto a resonant level of spinless fermions with an attractive interaction between the localized and extended states. We consider two such impurities at sites ${\mathbf{R}}_1$ and ${\mathbf{R}}_2$ interacting with each other via a hopping matrix element t and an interaction G between the localized fermions. The interactions t and G resemble the Ruderman-Kittel-Kasuya-Yosida interaction between the impurities. The physics of the model is most conveniently discussed in terms of even- and odd-parity states with respect to the point 1/2(${\mathbf{R}}_1$+${\mathbf{R}}_2$). We obtain the k-space renormalization-group equations for the model, which are integrated and discussed in terms of Ward cancellations. Finally, approximate expressions for the static and dynamical susceptibilities for the response to a homogeneous and staggered field are obtained. No dramatic anomalies are found, probably as a consequence of the broken spin-rotational invariance of the model.

• Received 19 September 1991

DOI:https://doi.org/10.1103/PhysRevB.45.4710