Fermionic parton theory of Rydberg Z₂ quantum spin liquids

Quantum spin liquids are novel highly entangled phases of matter that evade long-range order, even at absolute zero temperature. Experimentally, unambiguously identifying such an intricate quantum liquid state in solid-state materials is challenging. However, in recent years, programmable arrays of Rydberg atoms have emerged as a powerful tool for simulating strongly interacting quantum spin systems. For example, recent experiments on such a neutral-atom quantum simulator have demonstrated the realization of a Z₂ spin liquid phase on a ruby lattice [1]. This raises an important question about the precise microscopic nature of the phase realized on this quantum simulator.

Wen's projective symmetry group (PSG) framework provides an effective tool for characterizing such phases based on the parton representation of spins and the emergent gauge structure. In this study, we employ PSG classification to analyze fermionic parton mean-field states with a Z₂ low-energy gauge group on the ruby lattice. Considering a symmetry group that includes the full lattice space group and time-reversal symmetry, we identify 64 algebraic PSG solutions. However, when restricting interactions to third-nearest neighbors, only 50 of these solutions exhibit a low-energy Z₂ gauge group. By comparing the associated static structure factors to numerical computations, we find good qualitative agreement for one of the 50 Z₂ Ansätze, thus pointing to a promising candidate state for the one realized in experiments.

[1] Semeghini, G. et al. Probing topological spin liquids on a programmable quantum simulator. Science 374, 1242-1247 (2021).