Thouless quantum walks in topological flat bands.

Thouless quantum walks in topological flat bands. | 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 Thouless quantum walks in topological flat bands. Laura Pilozzi, Carlo danieli, Claudio Conti, Valentina Brosco This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6347811/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 Non-Abelian evolution is a landmark in modern theoretical physics. But if noncommutative dynamics has a significant impact in the control of entanglement and transport in quantum systems is an open question. Here we propose to utilize non-Abelian Thouless pumping in one-dimensional discrete-time quantum walks in lattices with degenerate Bloch-bands. We show how the interplay of non-commutativity and topology enables geometrically protected quantum coin and shift operators. By composing different non-Abelian pumping cycles, different classes of tunable protected quantum walks arise. Surprisingly, the walks break parity symmetry and generate a dynamic process described by a Weyl-like equation. Physical sciences/Optics and photonics Physical sciences/Physics Physical sciences/Optics and photonics/Optical physics Thouless pumping quantum computing Full Text Additional Declarations There is no conflict of interest Supplementary Files DanieliThQWsupplemental.pdf Supplementary material 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. 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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-6347811","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":441765118,"identity":"fb7c82dc-79bc-4602-b116-74ab9948c91b","order_by":0,"name":"Laura Pilozzi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYBACPijNA2YkVIBIxga8WthgWsCMhDNgLY149bChMBjbGAhbw8Z+xuzDD4Y7Mmzs7Y8/PJxnl2fewNz+AK8WnhzjmT0Mz3jYeA4kGCRuSy6WOUDQYTnGDDwMh3nYJBIOJCRuO5A4g6Bf+N8YM/4Ba0lsOJA4hxgtEjnGzBBbkhkbQLqI0PKsmFnGAOSXY8wMCceSE2cwMzbOwKeFnz95M+Obijv2/MAQ+/ijxi5xBnv7gw/4tECAwQEkDjNh9SBwgKCKUTAKRsEoGMEAAEsHQSYn7cROAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-1347-4550","institution":"CNR","correspondingAuthor":true,"prefix":"","firstName":"Laura","middleName":"","lastName":"Pilozzi","suffix":""},{"id":441765119,"identity":"9eae9af9-44f7-4a9a-a9b2-52a6ba1512f9","order_by":1,"name":"Carlo danieli","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Carlo","middleName":"","lastName":"danieli","suffix":""},{"id":441765120,"identity":"34918d95-2150-4872-9c56-5dc7db94e6bb","order_by":2,"name":"Claudio Conti","email":"","orcid":"https://orcid.org/0000-0003-2583-3415","institution":"Sapienza University of Rome","correspondingAuthor":false,"prefix":"","firstName":"Claudio","middleName":"","lastName":"Conti","suffix":""},{"id":441765121,"identity":"98c29a85-c034-4f5d-bd18-61601bdeb054","order_by":3,"name":"Valentina Brosco","email":"","orcid":"https://orcid.org/0000-0003-2738-5898","institution":"CNR - Istituto dei Sistemi Complessi","correspondingAuthor":false,"prefix":"","firstName":"Valentina","middleName":"","lastName":"Brosco","suffix":""}],"badges":[],"createdAt":"2025-03-31 21:25:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6347811/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6347811/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80642314,"identity":"6c3fe5c8-3294-4efc-8e41-8a530c17d3c3","added_by":"auto","created_at":"2025-04-15 13:27:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1695430,"visible":true,"origin":"","legend":"Article File","description":"","filename":"DanieliThQW.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6347811/v1_covered_5167cfa3-bcf1-49c1-bf61-bc5bb1f4219c.pdf"},{"id":80640820,"identity":"9f6e75bc-94b2-4c57-9317-41867dd7bec7","added_by":"auto","created_at":"2025-04-15 13:11:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2839890,"visible":true,"origin":"","legend":"Supplementary material","description":"","filename":"DanieliThQWsupplemental.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6347811/v1/db4c244c348b4e0a2abd347f.pdf"}],"financialInterests":"There is no conflict of interest","formattedTitle":"Thouless quantum walks in topological flat bands.","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"light-science-and-applications","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"lsa","sideBox":"Learn more about [Light: Science \u0026 Applications](http://www.nature.com/lsa/)","snPcode":"41377","submissionUrl":"https://mts-lsa.nature.com/","title":"Light: Science \u0026 Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Thouless pumping, quantum computing","lastPublishedDoi":"10.21203/rs.3.rs-6347811/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6347811/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Non-Abelian evolution is a landmark in modern theoretical physics. 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