Multiparty entanglement loops in quantum spin liquids

Multiparty entanglement loops in quantum spin liquids | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Multiparty entanglement loops in quantum spin liquids Liuke Lyu, Deeksh Chandorkar, Samarth Kapoor, So Takei, Erik S. Sørensen, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6960183/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Quantum spin liquids (QSLs) give rise to exotic emergent particles by weaving intricate entanglement patterns in the underlying electrons. Bipartite measures between subregions can detect the presence of anyons, but little is known about the full entanglement structure of QSLs. Here, we study the multiparty entanglement of QSLs via entanglement microscopy. We find that in contrast to conventional matter, the genuine multiparty entanglement (GME) between spins is absent in the smallest subregions, a phenomenon we call ``entanglement frustration.'' Instead, GME is more collective, and arises solely in loops. By exploiting exact results and large-scale numerics, we confirm these properties in various gapped and gapless QSLs realized in physically motivated Hamiltonians, as well as with string-net wavefunctions hosting abelian or non-abelian anyons. Our results shed new light on the phase diagram of Kitaev’s honeycomb model in a Zeeman field, and the Kagome Heisenberg model under various perturbations. Going beyond QSLs, we provide evidence that entanglement loops are a universal property of quantum gauge theories. This leads to a new understanding of fractionalization, and the means by which gauge bosons encode quantum information. Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena Physical sciences/Physics/Condensed-matter physics/Topological matter Physical sciences/Physics/Condensed-matter physics/Quantum fluids and solids Full Text Additional Declarations There is NO Competing Interest. Supplementary Files supplemental.pdf Supplemental Materials for Multipartite Entanglement in Quantum Spin Liquids Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6960183","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":484120276,"identity":"b62250fc-4945-46f4-9b0b-9122172f9e27","order_by":0,"name":"Liuke Lyu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7UlEQVRIiWNgGAWjYBACPmYGZiBlwcDA3gATY27AqRwE2CBaJBgYeA6A+AZAzEhACwNMi0QCsVrYeYwNPjBIJG64+cZ0w8cdf/L52Q82MPyowecwHuPEGSAtt3PMbs48Y2A5syexgbHnGH4th3mgWm7zthkYGBxIbGAGORivlj9gh52BaLE//xCo5R9+LckMIC03eKC2SABtYWzDp4Wt2LDHQMJ45pm0spsz24wNJG48bDjY24dbCz//4c0SPypsZPuOH95242ObnAF/f/LBBz++4dYCAQYMjg3I/AOENICAPTGKRsEoGAWjYIQCAKC1S0dkAHsUAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2444-6889","institution":"University of Montreal","correspondingAuthor":true,"prefix":"","firstName":"Liuke","middleName":"","lastName":"Lyu","suffix":""},{"id":484120277,"identity":"bec23930-9225-4fa1-ab31-01a299f2c13d","order_by":1,"name":"Deeksh Chandorkar","email":"","orcid":"","institution":"Department of Physics, Queens College of the City University of New York,","correspondingAuthor":false,"prefix":"","firstName":"Deeksh","middleName":"","lastName":"Chandorkar","suffix":""},{"id":484120278,"identity":"80742321-ae88-4fbb-944e-ee1e6737d2ca","order_by":2,"name":"Samarth Kapoor","email":"","orcid":"","institution":"Department of Physics, Queens College of the City University of New York,","correspondingAuthor":false,"prefix":"","firstName":"Samarth","middleName":"","lastName":"Kapoor","suffix":""},{"id":484120279,"identity":"2e8d860a-1b6d-4d57-b363-1293abb225b0","order_by":3,"name":"So Takei","email":"","orcid":"","institution":"Queens College of the City University of New York","correspondingAuthor":false,"prefix":"","firstName":"So","middleName":"","lastName":"Takei","suffix":""},{"id":484120280,"identity":"7853d38d-fde5-4d21-a70c-22ae4faff29f","order_by":4,"name":"Erik S. 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