The rapid advancement of quantum science and technology has established Rydberg atom arrays as a premier platform for exploring quantum many-body physics with exceptional precision and controllability. Traditionally, each atom is modeled as a spin degree of freedom with its spatial motion effectively frozen. This simplification has facilitated the discovery of a rich variety of novel equilibrium and non-equilibrium phases, including Z₍ symmetry-breaking orders and quantum scars. In this work, we investigate the consequences of incorporating atomic vibrations in optical tweezers, which give rise to spin-phonon coupling. For systems in thermal equilibrium, we find that this coupling leads to a new symmetry-breaking phase in the weak driving limit, as a result of induced three-spin interactions. Furthermore, we show that the violation of quantum thermalization in Z₂-ordered states is suppressed when spin-phonon coupling is introduced. Our results are readily testable in state-of-the-art Rydberg atom array experiments.
Zhang et al. (2025) studied this question.