Asymmetry effects on the phases of RKKY-coupled two-impurity Kondo systems

In a related work [Phys. Rev. B 107, L121111 (2023)], we have shown that, in the two-impurity Anderson model with two hosts coupled by spin exchange in the most symmetric case, there are either two phase transitions or none. The phases comprise the conventional Kondo and RKKY regimes and a different one, interpreted as a Kondo-stabilized, metallic quantum spin liquid. Here, we analyze how various types of asymmetry affect this picture. We demonstrate that the transitions are robust against the coupling and particle-hole asymmetries, provided charge transfer is forbidden. This holds true despite the scattering phase shift at each impurity taking nonuniversal values. Finally, for an extended model including charge transfer between the hosts and a small Coulomb interaction at the host sites directly coupled to impurities, we show that the presence of charge transfer changes the phase transitions into crossovers. Provided the interhost hopping is sufficiently small, this leads to qualitatively the same physics at nonzero temperature. The relevance of this model for rare-earth atoms in a metallic host is discussed, and potential experimental setups for observing our findings are proposed.