Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array*

Motivated by recent experimental realizations of exotic phases of matter on programmable quantum simulators, we carry out a detailed theoretical study of quantum phase transitions in a Rydberg atom array on a square lattice, with both open and periodic boundary conditions. In the bulk, we discover first-order transitions from the disordered paramagnetic phase to the density-wave-ordered star and striated phases. We develop an understanding of these first-order transitions using the framework of Landau-Ginzburg-Wilson theory. Remarkably, we find that with open boundary conditions, the boundary itself  undergoes a second-order quantum phase transition, independent of the bulk. These results explain recent experimental observations and provide important insights for the adiabatic state preparation of novel quantum phases and quantum optimization using Rydberg atom array platforms.