Low energy excitations of two 2D frustrated bilayer quantum magnets

We study the low energy spectra of bilayer versions of the Kitaev honeycomb and the J_1-J_2-Heisenberg square lattice model, introducing an interlayer Heisenberg exchange. We explore the phase diagram of these models using series expansions obtained through perturbative Continuous Unitary Transformation (pCUT) starting in the quantum-dimer phase at strong interlayer coupling. Focusing on the low energy excitations, we calculate spectra up to and including two-triplon states. For the Kitaev bilayer, we also investigate the two-triplon zero temperature Raman scattering as an experimental probe. Extrapolating our calculated one-triplon dispersions, we use Padé and dLog-Padé pproximations as well as a varied Euler resummation to map out quantum critical lines from the dimer phase to various other phases. In the two-triplon sector, we uncover several collective (anti)bound states for both models and provide direct physical pictures explaining their occurrence. Further, we examine their dependence on the spin components, the exchange parameters, and, for the Kitaev model, the bilayer stacking variations. Contrasting our results to various limiting cases already discussed in the literature, we find good agreement. As compared to existing knowledge, our work expands the insights qualitatively and quantitatively onto a much larger part of the bilayer parameter space for both models. Particularly interesting findings include, a very strong sensitivity of the Raman intensity on the scattering geometry for the Kitaev bilayer model as well as a large impact of two-triplon interactions on this intensity. Moreover, for the J_1-J_2 bilayer, we provide evidence, that for J_2/J_1 > 0.5 a close-by condensation of one-triplon and two-triplon singlet bound states is possible, suggesting the presence of additional phases between dimer and collinear state.