We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous one-dimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbors are unexcited. We show that the RCA201 (Floquet-PXP) model exhibits ballistic propagation of interacting quasiparticles—or solitons—corresponding to the domain walls between nontrivial threefold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the nonequilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.

• Received 8 July 2020
• Revised 28 October 2020
• Accepted 30 October 2020

DOI:https://doi.org/10.1103/PhysRevE.102.062107