Exact solution of the Floquet-PXP cellular automaton

Wilkinson, Joseph W. P.; Klobas, Katja; Prosen, Toma�; Garrahan, Juan P.

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 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.

Citation

Wilkinson, J. W. P., Klobas, K., Prosen, T., & Garrahan, J. P. (2020). Exact solution of the Floquet-PXP cellular automaton. Physical Review E, 102(6), Article 062107. https://doi.org/10.1103/PhysRevE.102.062107

• Journal Article Type: Article
• Acceptance Date: Oct 30, 2020
• Online Publication Date: Dec 3, 2020
• Publication Date: Dec 3, 2020
• Deposit Date: Jan 5, 2021
• Publicly Available Date: Jan 5, 2021
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 102
• Issue: 6
• Article Number: 062107
• DOI: https://doi.org/10.1103/PhysRevE.102.062107
• Public URL: https://nottingham-repository.worktribe.com/output/5201361
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.062107
• Additional Information: ©2020 American Physical Society