  In a related work [arXiv:2106.07519] we have shown that in the two-impurity
Anderson (2iA) 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 novel one, interpreted
as a Kondo-stabilized, metallic quantum spin liquid (QSL). 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 non-universal 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 inter-host hopping is sufficiently small, this leads to
qualitatively the same physics at non-zero 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.
