Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics
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Quantum Physics arXiv:2606.11561 (quant-ph) [Submitted on 10 Jun 2026] Title:Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics Authors:Hanchen Liu, Tianci Zhou, Xiao Chen View a PDF of the paper titled Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics, by Hanchen Liu and 2 other authors View PDF HTML (experimental) Abstract:Participation entropy (PE) quantifies the spread of a many-body wavefunction across configuration space. While PE relaxes rapidly in generic chaotic systems, we show that $\mathrm{U}(1)$ conservation laws slow it down by imprinting with the slow hydrodynamic modes. Using a cluster expansion around equilibrium, we show that, after local density inhomogeneities decay, the leading PE deficit is dominated by squared connected density correlations. The long time relaxation is therefore controlled by diffusive correlation spreading, giving $\Delta S(t)\sim t^{-1/2}$ in the hydrodynamic regime and crossing over to $\sim \exp[-O(t/L^2)]$ when $t\geq L^2$. We confirm this entropy correlation relation using exact computation and infinite system tensor network simulations in various quantum $\mathrm{U}(1)$ conserving circuits. Our results establish PE as a sensitive probe of hydrodynamic memory and suggest that slow relaxation is a generic consequence of conservation laws. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2606.11561 [quant-ph] (or arXiv:2606.11561v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.11561 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hanchen Liu [view email] [v1] Wed, 10 Jun 2026 01:40:54 UTC (2,210 KB) Full-text links: Access Paper: View a PDF of the paper titled Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics, by Hanchen Liu 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.stat-mech 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?)