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We investigate the nature of quantum phases arising in chiral interactingHamiltonians recently realized in Rydberg atom arrays. We classify all possiblefermionic chiral spin liquids with $\mathrm{U}(1)$ global symmetry using partonconstruction on the honeycomb lattice. The resulting classification includessix distinct classes of gapped quantum spin liquids: the correspondingvariational wave functions obtained from two of these classes accuratelydescribe the Rydberg many-body ground state at $1/2$ and $1/4$ particledensity. Complementing this analysis with tensor network simulations, weconclude that both particle filling sectors host a spin liquid with the sametopological order of a $\nu=1/2$ fractional quantum Hall effect. At density$1/2$, our results clarify the phase diagram of the model, while at density$1/4$, they provide an explicit construction of the ground state wave functionwith almost unit overlap with the microscopic one. These findings pave the wayto the use of parton wave functions to guide the discovery of quantum spinliquids in chiral Rydberg models.

Classification and emergence of quantum spin liquids in chiral Rydberg models