Study of the instability of the single-impurity multichannel ground state to inter-impurity interactions

We study a two-impurity, two-channel Kondo model, focusing on the behavior near the limit of two independent impurities. We find that significant departures from the independent regime develop below a crossover temperature which scales approximately as the tenth power of a parity asymmetry. The one-impurity, two-channel Kondo model has been the object of much renewed interest recently [ i ] . The importance of this model is the stable non-Fermi liquid ground state that occurs when the coupling constants of the two channels are equal. One way to investigate the robustness of the ground state is to study the effects of adding a second impurity some finite distance from the first. Numerical renormalization group results I-2] indicate that the additional interactions induced by a second impurity destabilize the single-impurity point in all phase-space directions. In this paper we study the region in phase space around the single-impurity point where destabilization is taking place. In particular we will discuss two aspects: scaling along the vertical ( J e Jo) axis (all terms to be defined below) and the shape of the boundary between the marginal and Kondo ground state behavio,. The model we study is of two spin-l/2 impurities interacting directly with two channels of conduction electrons, and indirectly, via RKKY interactions, with each other. The Hamiltonian is H ~ ; d 3 " Y s~,r,)'S, = kr, k~kc#Ckc # J (1)