Quantum magnetism in ultracold atomic systems

Frustrated quantum magnets have long been happy hunting grounds for strongly correlated many-body physics. Today, interacting arrays of Rydberg atoms provide a new route to realize models of Ising quantum magnets, providing versatile platforms for exploring exotic many-body phases and their dynamics. Motivated by recent experimental advances, we 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 elusive topological spin liquid states with fractionalized excitations that have been proposed as ground states of various spin-1/2 magnets. We also highlight the emergence of new spin liquid states with more complex gauge groups, such as U(1)xU(1), as well as higher spin models, and discuss their realization in present-day neutral atom platforms.