Generalized Schrieffer-Wolff transformation of the two-impurity Kondo model

We have carried out a generalized Schrieffer-Wolff transformation of an Anderson two-impurity Hamiltonian to study the low-energy spin interactions of the system. The 2nd-order expansion yields the standard Kondo Hamiltonian for two impurities with additional scattering terms. At 4th order, we get the well-known RKKY interaction. In addition, we also find an antiferromagnetic superexchange coupling, and a previously undiscovered correlated Kondo coupling between the two impurities