Quantum phases of Rydberg atoms in two-dimensional arrays

We describe the zero-temperature phases of two-dimensional arrays of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out detailed phase diagrams and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body physics. We also discuss how Rydberg atom arrays can be a natural platform for probing topological phenomena based on appropriate lattice geometries and innate interactions, even without engineering specific gauge constraints.