  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.
