Localization and criticality in antiblockaded 2D Rydberg atom arrays

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. We study the effect of positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade conditions. We show that this condition leads to the connectivity of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. We consider positional disorder that is naturally present in realistic Rydberg atom arrays. Remarkably, we find three distinct regimes in the phase diagram as the disorder strength is varied: a critical phase, a delocalized but nonergodic phase, and a phase with a disorder-induced flat band. The critical phase's existence depends crucially upon the singular flat band in our model, and is absent in any 1D system. We propose to use quench dynamics to probe the three different regimes experimentally.