The quantum phases of square lattice Rydberg atom arrays

We report on the ground state phase diagram of interacting Rydberg atoms in a two dimensional square lattice array, a promising platform for quantum information processing. Using new developments in tensor network algorithms, we are able to study with high fidelity the phases in the bulk as well as their analogs in large, experimentally accessible finite arrays by including all long-range interactions. We find that much of the phase diagram consists of crystalline and quantum mean-field-like ground states, akin to proposals in the literature although significantly altered in our high-accuracy treatment. However, we also discover a hitherto hidden region of an unusual ordered quantum phase with non-trivial entanglement. Broadly, our results yield a conceptual guide for future experiments, including where to look for interesting physics.