Two Anderson Impurities in the Kondo Limit. Systematic Study

We analyze the two Anderson impurity problem, in the strong Coulomb repulsion limit, by means of variational wave functions whose equations we solve analytically. We found two pairs of Doublet states, one odd and one even with respect to the midplane between the impurities. These Doublets make a significatively strong use of the hybridization terms of the Hamiltonian, and have a much larger Kondo-like correlation energy than a single impurity (the Kondo energy). Furthermore, these Doublets combine to form a Super-Singlet. This Super-Singlet makes use of the remaining hybridization probability to improve its energy with respect to the Doublets energy, but for low-Dimensional systems and at the inter-impurity distances where the Doublets are full developed, its energy gain is exponentially small. The interaction behind the Doublets is a first-order (in the effective Kondo coupling) one, it also generates a parallel alignment of the impurity-spins. This ferromagnetic impurity-impurity response is thus generated without resort to the RKKY interaction. The effective range of this first-order Doublet interaction is also much larger than the one of the RKKY interaction.