The sub-ballistic spread of correlations and a minimal random spin model on a Rydberg quantum simulator

Rydberg atom arrays with Van der Waals interactions are theoretically expected to simulate the physics of locally connected transverse-field Ising model (TFIM), a paradigmatic model of statistical mechanics. We remotely operate the analogue Rydberg simulator of QuEra Computing, and experimentally test this theoretical prediction far from equilibrium. The Rydberg simulator exhibits sub-ballistic spread of correlations, instead of ballistic, and logarithmic scaling of entanglement entropy in time, instead of linear, while retaining its initial magnetization. We trace the origin of this experimental observation to the atom motion in tweezer traps with tensor network modeling. The atom motion leads to an effective and natural disorder parameter in a minimal random spin model that we introduce to characterize the TFIM limit of the Rydberg atom arrays. We further explore different dynamical regimes of this many-body system by utilizing the minimal model. Our work highlights the role of atom motion in the many-body dynamics of Rydberg atom arrays when the simulator is operated at its TFIM limit, and proposes simple benchmarking experiments far from equilibrium to test for its effect.