Operator growth and eigenstate entanglement in an interacting integrable Floquet system

Understand

We analyze a simple model of quantum dynamics, which is a discrete-time deterministic version of the Frederickson-Andersen model.

• We argue that this model is integrable, with a quasiparticle description related to the classical hard-rod gas.
• Despite the integrability of the model, commutators of physical operators grow as in generic chaotic models, with a diffusively broadening front, 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 scale that is parametrically smaller than half the system size.