Chiral Spin Liquid in a hexagonal Lattice of Rydberg Atoms with density-dependent Peierls Phases

Recently, experiments demonstrated that spin-orbit coupling in systems of Rydberg atoms gives rise to Peierls phases in the hopping of Rydberg excitations that feature a density-dependence [Lienhard et al., PRX 10, 021031 (2020)]. In this talk we expand on this concept and analyze theoretically a two-dimensional hexagonal (honeycomb) lattice of identical spin-orbit coupled Rydberg atoms exhibiting density-dependent hopping terms. We numerically investigate the phase diagram by modifying the strength of the density-dependent terms and propose order parameters to identify the phase transitions. In the regime where density-dependent and direct hopping processes are comparable in strength, we find evidence for a chiral spin liquid (CSL) phase.