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We analyze a simple model of quantum dynamics, which is a discrete-timedeterministic version of the Frederickson-Andersen model. We argue that thismodel is integrable, with a quasiparticle description related to the classicalhard-rod gas. Despite the integrability of the model, commutators of physicaloperators grow as in generic chaotic models, with a diffusively broadeningfront, and local operators obey the eigenstate thermalization hypothesis (ETH).However, large subsystems violate ETH; as a function of subsystem size,eigenstate entanglement first increases linearly and then saturates at a scalethat is parametrically smaller than half the system size.

Operator growth and eigenstate entanglement in an interacting integrable Floquet system