Generalized Schrieffer-Wolff Transformation of 2 Kondo Impurity Problem
  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 second-order expansion yields the standard Kondo Hamiltonian for two impurities with additional scattering terms. At fouth-order, we get the well-known RKKY interaction. In addition, we also find an antiferromagnetic superexchange coupling and a correlated Kondo coupling between the two impurities. 
T. Tzen Ong (1 and 2) and B. A. Jones (2) ((1) Department of Applied   Physics, Stanford University, (2) IBM Almaden Researc...