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Spectral properties of the two-impurity Anderson model with varying distance and various interactions

We present a novel approximation for two interacting magnetic impurities immersed into a noninteracting metallic host. The scheme is based on direct perturbation theory in the hybridization between the impurity and band electrons. This two-impurity enhanced noncrossing approximation (TIE) fully incorporates the indirect interaction between the impurities which are mediated by the conduction electrons as well as additional arbitrary direct interaction matrix elements. We qualify the approximation by investigating the uncoupled case and conclude the TIE to be equally accurate as its single impurity counterpart. The physical properties of the two-impurity Anderson model are first investigated in some limiting cases. In a regime, where each of the uncoupled two impurities would exhibit a pronounced Kondo effect, we ignore the indirect coupling via the conduction band and only incorporate direct interactions. For a ferromagnetic direct exchange coupling, the system displays a behavior similar to a spin-one Kondo effect, while an antiferromagnetic coupling competes with the Kondo effect and produces a pseudogap in the many-body Kondo resonance of the single-particle spectral function. Interestingly, a direct one-particle hopping also produces a pseudogap but additionally pronounced side-peaks emerge. This gap is characteristically different from the case with antiferromagnetic coupling, since it emerges as a consequence of distinct Kondo effects for the bonding and anti-bonding orbital, i.e.\ it reflects a splitting of even and odd parity states.For the general case of only indirect coupling the results show signatures of all the previously discussed limiting cases as function of the impurity-impurity distance. We are led to the conclusion that the well known Doniach-scenario captures essential aspects this model, but the details especially at small distances are more complicated.