Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization
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Quantum Physics arXiv:2601.01327 (quant-ph) [Submitted on 4 Jan 2026] Title:Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization Authors:Chun-Yue Zhang, Shi-Xin Zhang, Zi-Xiang Li View a PDF of the paper titled Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization, by Chun-Yue Zhang and Shi-Xin Zhang and Zi-Xiang Li View PDF HTML (experimental) Abstract:Characterizing the intricate structure of entanglement in quantum many-body systems remains a central challenge, as standard measures often obscure underlying geometric details. In this Letter, we introduce a powerful framework, termed multi-bipartition entanglement tomography, which probes the fine structure of entanglement across an exhaustive ensemble of distinct bipartitions. Our cornerstone is the discovery of a ``bond-additive law'', which reveals that the entanglement entropy can be precisely decomposed into a bulk volume-law baseline plus a geometric correction formed by a sum of local contributions from crossed bonds of varying ranges. This law distills complex entanglement landscapes into a concise set of entanglement bond tensions $\{\omega_j\}$, serving as a quantitative fingerprint of interaction locality. By applying this tomography to Hamiltonian dynamics, random quantum circuits, and Floquet dynamics, we resolve a fundamental distinction between thermalization mechanisms: Hamiltonian thermalized states retain a persistent geometric imprint characterized by a significantly non-zero $\omega_1$, while this structure is completely erased in random quantum circuit and Floquet dynamics. Our work establishes multi-bipartition entanglement tomography as a versatile toolbox for the geometric structure of quantum information in many-body systems. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2601.01327 [quant-ph] (or arXiv:2601.01327v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.01327 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Chun-Yue Zhang [view email] [v1] Sun, 4 Jan 2026 01:59:52 UTC (4,953 KB) Full-text links: Access Paper: View a PDF of the paper titled Bond Additivity and Persistent Geometric Imprints of Entanglement in Quantum Thermalization, by Chun-Yue Zhang and Shi-Xin Zhang and Zi-Xiang LiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.dis-nn cond-mat.str-el 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)