  Magnetic adatoms on a superconducting substrate undergo a quantum phase
transition as their exchange coupling to the conduction electrons increases.
For quantum spins, this transition is accompanied by screening of the adatom
spin. Here, we explore the consequences of this screening for the phase
diagrams and subgap excitation spectra of dimers of magnetic adatoms coupled by
hybridization of their Yu-Shiba-Rusinov states and spin-spin interactions. We
specifically account for higher spins, single-ion anisotropy,
Ruderman-Kittel-Kasuya-Yosida coupling, and Dzyaloshinsky-Moriya interactions
relevant in transition-metal and rare-earth systems. Our flexible approach
based on a zero-bandwidth approximation provides detailed physical insight and
is in excellent qualitative agreement with available numerical-renormalization
group calculations on monomers and dimers. Remarkably, we find that even in the
limit of large impurity spins or strong single-ion anisotropy, the phase
diagrams for dimers of quantum spins remain qualitatively distinct from phase
diagrams based on classical spins, highlighting the need for a theory of
quantum Yu-Shiba-Rusinov dimers.
