Unveiling the S=3/2 Kitaev honeycomb spin liquids

Recently, material realizations of the spin 3/2 Kitaev honeycomb model have been proposed, but the model has not been solved by either analytical or numerical methods. Here the authors report exact results for the spin 3/2 model consistent with numerical simulations, and find gapped and gapless quantum spin liquids. The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z(2) gauge field. Employing an SO(6) Majorana representation of spin3/2's, we find an exact representation of the conserved plaquette fluxes in terms of static Z(2) gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by the addition of a [001] single ion anisotropy (SIA) which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak [111] SIA, we discuss an emergent chiral QSL within a perturbation theory.