The two-impurity Anderson model: Results of a perturbative expansion in U

We discuss the results of a study of the two-impurity Anderson model carried out by using a perturbative expansion in U, which is known to provide a power expansion of the exact solution in the one-impurity case. The results presented concern the uniform and staggered susceptibilities, the instantaneous spin-spin correlations [S1.S2], the impurity self-energy and spectral density, the linear coefficient of the impurity specific heat (gamma), and the Wilson's ratio. The calculations are performed up to second order in the interaction, and for the nearly ''symmetric'' case. Most of the quantities investigated display 2k(F)R oscillations as a function of the impurity separation R, with a series of regions of ferromagnetic and antiferromagnetic correlations between the spins, which are quite independent of the value of the interaction U. The uniform susceptibility and the linear coefficient of the specific heat are enhanced (suppressed) in correspondence with regions of ferromagnetic (antiferromagnetic) correlations. Moreover, we find that the oscillations in the static susceptibilities tend to increase considerably with increasing U, and conjecture that this increase might lead to large oscillations in the Kondo regime. These oscillations would be the hallmark of strong Ruderman-Kittel-Kasuya-Yosida interactions in a Fermi-liquid (Kondo) ground state. We also find that the Wilson ratio has a rich nonuniversal behavior, confirming previous investigations on the two-impurity Kondo model. The relevance of these results and the connection with the literature is discussed.