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.

中文翻译：

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Floquet-PXP细胞自动机的精确解决方案

我们研究了一个整体确定性Floquet模型（规则201同步一维可逆细胞自动机（RCA201））的动力学。该系统与PXP模型的确定性，可逆性和离散版本相对应，从而仅当两个站点的最近邻居都未激发时，站点才会翻转。我们显示，RCA201（Floquet-PXP）模型展现出与非平凡三重真空状态之间的畴壁相对应的相互作用准粒子（或孤子）的弹道传播。从准粒子图开始，我们找到了一系列边界条件（包括周期和随机）的非平衡平稳态的精确矩阵乘积态形式。我们讨论了模型可集成性的进一步含义。