Two-triplon excitations of the Kitaev-Heisenberg bilayer

We study the spectrum of a bilayer Kitaev magnets on honeycomb lattice, coupled by Heisenberg exchange in quantum-dimer phase at strong interlayer coupling. Using perturbative Continuous Unitary transformation (pCUT) we perform series expansion starting from fully dimerized limit, to evaluate elementary excitations, reaching up and focusing two-triplon sector. In stark contrast conventional quantum magnets, because broken $SU(2)$-invariance, encoded intralayer directional compass-exchange, magnet is shown exhibit rich structure scattering-state continua, as well several collective (anti)bound states. Direct physical pictures for occurrence latter are provided states studied versus stacking type, spin components, parameters. addition spectra, investigate corresponding experimental probe evaluating magnetic Raman-scattering intensity. find very sensitivity this intensity interactions scattering geometry, however signal appears only close proximity continuum.