Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms

We perform unbiased quantum Monte Carlo simulations of quantum Ising models defined on amorphous arrays of Rydberg atoms, motivated by a recent proposal for their experimental realization using engineered configurations of the optical tweezers. In contrast to previous studies focusing on periodic geometries, our models are designed to possess well-controlled local structural properties while lacking long-range order. We identify a quantum phase transition from a paramagnetic to a spin-glass phase, characterized via the Edwards-Anderson order parameter computed from the replica overlap. The magnetic structure factor reveals short-range, isotropic antiferromagnetic correlations, and the spin-overlap distribution exhibits a nontrivial form with two broad peaks and significant weight at zero overlap. A comparison with the clean kagome lattice, which shares similar local geometry, underscores the critical role of amorphous structure in stabilizing the spin-glass phase. Our results suggest a promising pathway for the experimental realization of quantum spin glasses using programmable Rydberg atom arrays.