From composite particles to lattice gauge theories in systems 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 vacancies that carry flux quanta reminiscent of composite particles found in fractional quantum Hall systems. Experiments have recently shown [Lienhard et al., Phys. Rev. X, 10, 021031 (2020)] that spin-orbit coupling in Rydberg systems breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of the hard-core bosonic excitations or equivalently to complex XY spin interactions. We numerically investigate the time evolution of such a system at different fillings and find that vacancies on one sublattice act as local magnetic impurities to excitations on the other sublattice. We also consider the chiral (edge) motion of the magnetic impurities and the emergence of an Abrikosov-type vortex lattice. Lastly, we discuss the implications for possible anyonic quasiparticles in the system and applications to simple lattice gauge theories.