Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays

Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter. On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize. Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian - a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics. Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade. Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs. We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations. We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.