Abstract
Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.
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