Exact solution of the Floquet-PXP cellular automaton

Joseph W. P. Wilkinson; Juan P. Garrahan; Katja Klobas; Toma\v{z} Prosen

Exact solution of the Floquet-PXP cellular automaton

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arxiv 2006.06556 v1 pith:TLA5IQYF submitted 2020-06-11 cond-mat.stat-mech

Joseph W. P. Wilkinson , Katja Klobas , Tomaž Prosen , Juan P. Garrahan This is my paper · ORCID

classification cond-mat.stat-mech

keywords modelautomatoncellulardeterministicexactfloquet-pxprca201reversible

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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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Weak ergodicity breaking with isolated integrable sectors
cond-mat.stat-mech 2024-12 accept novelty 7.0 of 10

Isolated integrable subspaces can be embedded non-trivially into chaotic spin chains; all examples are perturbations of Hilbert-space-fragmented models.

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