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 nonequilibrium phases, including ${\mathbb{Z}}_{\text{N}}$ 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 ${\mathbb{Z}}_2$-ordered states is suppressed when spin-phonon coupling is introduced. Our results are readily testable in state-of-the-art Rydberg-atom array experiments.

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• Cold gases in optical lattices
• Rydberg gases
• Rydberg atoms & molecules
• Trapped atoms