Emergent Z₂ gauge theories and topological excitations in Rydberg quantum simulators

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 theoretically investigate the quantum phases that can be realized by such Rydberg atom simulators in two dimensions. We show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z₂ gauge theories endowed with matter fields. Based on this mapping, we demonstrate how Rydberg platforms can be used to realize topological spin liquid states based solely on their native van der Waals interactions. We also discuss the nature of the fractionalized excitations of two distinct classes of such Z₂ quantum spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.