Two-dimensional Rydberg Gases and the Quantum Hard-Squares Model

We study a two-dimensional lattice gas of atoms that are photoexcited to Rydberg states in which they interact via the van der Waals interaction. We explore the regime of dominant nearest-neighbor interaction where this system is intimately connected with a quantum version of Baxter's hard-squares model. We show that the strongly correlated ground state of the Rydberg gas can be analytically described by a projected entangled pair state that constitutes the ground state of the quantum hard-squares model. This correspondence allows us to identify a phase boundary where the Rydberg gas undergoes a transition from a disordered (liquid) phase to an ordered (solid) phase.