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arXiv · 2006.06556

Exact solution of the Floquet-PXP cellular automaton

Joseph W. P. Wilkinson·Katja Klobas·Tomaž Prosen·Juan P. Garrahan
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Abstract

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 neighbours are unexcited. We show that the RCA201/Floquet-PXP model exhibits ballistic propagation of interacting quasiparticles - or solitons - corresponding to the domain walls between non-trivial three-fold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the non-equilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.

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Joseph W. P. Wilkinson, Katja Klobas, Tomaž Prosen, Juan P. Garrahan. 2020-06-11. Exact solution of the Floquet-PXP cellular automaton. https://doi.org/10.1103/physreve.102.062107

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