Identifying slow relaxation in many-body quantum systems through state-graph geometry and state-graph heterogeneity

Quantum Physics arXiv:2608.05298 (quant-ph) [Submitted on 5 Aug 2026] Title:Identifying slow relaxation in many-body quantum systems through state-graph geometry and state-graph heterogeneity Authors:Heiko Georg Menzler, Tom Ben-Ami View a PDF of the paper titled Identifying slow relaxation in many-body quantum systems through state-graph geometry and state-graph heterogeneity, by Heiko Georg Menzler and 1 other authors View PDF HTML (experimental) Abstract:We adapt tools from the theory of quantum random walks to investigate slow relaxation dynamics through the many-body state graph. Specifically, we construct a probe of heterogeneity between basis states defined using hitting times derived from the unitary time-evolution operator. We find that the state-graph geometry, encoded by the pairwise hitting time of basis states, is a highly sensitive indicator of slow relaxation dynamics in a variety of systems. We study three paradigmatic models: the Rosenzweig-Porter model, the quantum East model, and the triangular lattice gas model, exhibiting a sudden onset of slow dynamics upon tuning of a control parameter. As a global characterization of the graph geometry, we analyze the spectral radius of the hitting matrix. We find that it increases sharply at the onset of slow dynamics, spanning many orders of magnitude, with a characteristic crossing point at the transition. Our work provides a geometric framework for describing and identifying phases with slow relaxation using a unified graph-theoretic formalism. Comments: Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2608.05298 [quant-ph] (or arXiv:2608.05298v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.05298 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tom Ben-Ami [view email] [v1] Wed, 5 Aug 2026 18:00:32 UTC (2,336 KB) Full-text links: Access Paper: View a PDF of the paper titled Identifying slow relaxation in many-body quantum systems through state-graph geometry and state-graph heterogeneity, by Heiko Georg Menzler and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.quant-gas 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?)