Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model
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Quantum Physics arXiv:2606.19430 (quant-ph) [Submitted on 17 Jun 2026] Title:Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model Authors:Xiao-Yang Yang, He-Ran Wang, Zhong Wang View a PDF of the paper titled Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model, by Xiao-Yang Yang and 2 other authors View PDF HTML (experimental) Abstract:Studies of integrable systems have profoundly deepened the fundamental understanding of quantum many-body physics. While equilibrium properties such as ground states and thermodynamics can often be characterized efficiently, accurately characterizing nonequilibrium integrable dynamics remains a significant challenge. Here, we address this problem in the "Rule 201" quantum cellular automaton, an integrable Trotterization of the PXP Hamiltonian. Using the tensor-network approach of the influence matrix, we develop local conditions called generalized zipper conditions that allow exact solutions of local dynamics. We also introduce a numerical bootstrap method for solving influence matrices with finite but relatively large bond dimensions. This uncovers a rich landscape of nonequilibrium behavior exhibiting initial-state dependence. As an example, we investigate the fate of persistent oscillating dynamics under local non-integrable perturbations, and present analytical results for non-thermal relaxation constrained by conservation laws. We also obtain numerically exact results for entanglement growth across a broad class of initial states. Furthermore, from an information-theoretic perspective, we identify a refined structure of multitime correlations termed the hidden Markov order: the memory encoded in the dynamics separates into finite-length and long-range distributed components, which becomes transparent in an exact split-index matrix-product-state representation of the influence matrix. Our approach enables unified investigations of nonthermalizing and thermalizing regimes of nonequilibrium dynamics within a single analytically tractable model, and can be tested experimentally in state-of-the-art quantum simulators such as Rydberg atom arrays. Comments: Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph) Cite as: arXiv:2606.19430 [quant-ph] (or arXiv:2606.19430v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.19430 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: He-Ran Wang [view email] [v1] Wed, 17 Jun 2026 18:00:01 UTC (5,525 KB) Full-text links: Access Paper: View a PDF of the paper titled Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model, by Xiao-Yang Yang and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.quant-gas cond-mat.str-el math math-ph math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)