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

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit coupled Rydberg atoms gives rise to disordered quantum phases which are candidates for topological quantum spin liquids. As recently demonstrated in [Lienhard et al., Phys. Rev. X, 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of the hard-core bosons or equivalently to complex XY spin interactions. We numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms. In the regime where the two terms are comparable, we find a disordered quantum state that is absent in a mean-field description. This phase is characterized by a finite spin-gap, a large spin chirality as well as a many-body Chern number C=1. We therefore identify this phase as a topological spin liquid.