Thermodynamic scaling theory for the two-impurity anderson model

Abstract

We present results of a study of the two-impurity Anderson model using a thermodynamic scaling theory developed recently. The model is characterized by the Coulomb energy U, the orbital energy εd, the d-level width Γ, and the separation between impurities R. If Γ«-εd«U, the low-temperature physics maps onto that of the two-impurity Kondo problem, discussed by us elsewhere; the main difference is that the RKKY interaction can acquire an antiferromagnetic contribution with a (k_FR)^-2 envelope over a restricted range of k_FR. In this case impurity-impurity interactions can be substantial. The other interesting case is when the impurities have a "fluctuating valence" with the singlet lying lower in energy, i.e., εd~Γ. Here we find that the single-impurity physics dominates the low-temperature behavior, and impurity-impurity interactions are perturbative. The qualitative features of the temperature-dependent susceptibility are discussed.