Non-interacting two-impurity Anderson model on a lattice at particle-hole symmetry

We study the non-interacting two-impurity Anderson model on a lattice using the Green function equation-of-motion method. We focus on the RKKY limit that is characterized by a small hybridization between impurities and host electrons and the absence of a direct coupling between the impurities. Odd and even channels do not decouple, in general. Different real parts of the hybridization functions lead to a small splitting of the single-impurity resonance. Along the axes, the RKKY interaction energy decays proportional to the inverse square of the impurity separation. Hence, the RKKY approximation to the RKKY interaction is inadequate. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim