Two-impurity Anderson model: some exact results within Fermi liquid theory

We present exact expressions for the conduction electron phase shifts for the two-impurity Anderson model in terms of the impurity Green functions. We show that, for the symmetric model, to all orders in the perturbation theory in U, the only allowed value of the phase shifts is π/2. It is also shown that, quite generally, a vanishing of the phase shifts (signaling a RKKY phase) must be associated with the development of a gap in the impurity single particle excitation spectrum. In the symmetric case this is in turn associated with a divergence of the linear coefficient of the heat capacity. The implications of these results on the physics of the transition from Kondo to RKKY phases are briefly discussed.