Strongly-interacting Integrable Floquet Hopping models from Rydberg blockade

In this paper, we introduce a class of strongly-interacting Floquet models, whose single-particle dynamics are equivalent to bosonic hopping models. We propose to experimentally realize strongly interacting versions of these using Rydberg atom arrays, where the interactions arise from the Rydberg blockade effect. We do this by developing a gate which conserves both particle number and respects the Rydberg blockade, dynamically conserving two U(1) charges. We study in detail the dynamics in a 1D chain, and identify a large class of integrable classical cellular automata. We prove integrability via a coordinate Bethe Ansatz solution, and harness the classical cellular automata description of the dynamics to gain insight into its origin. Remarkably, these automata remain integrable to natural quantum deformations, resulting in a large class of integrable quantum cellular automata. Using the thermodynamic Bethe Ansatz, we analyze the expected behavior of experimentally realizable quenches within the framework of generalized hydrodynamics, and find unusual diffusive behaviors in certain parameter regimes.