Neural spectroscopy reveals structure from a learned vacuum

Neural spectroscopy reveals structure from a learned vacuum | 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Download PDF Article Neural spectroscopy reveals structure from a learned vacuum Daeho Park This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9575599/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Excited states encode the mechanisms of interacting quantum systems and the structure of the underlying theory. But in first-principles calculations they are generally much harder to extract and interpret reliably than ground states. Neural-network wavefunctions have expanded access to ground states, yet excited-state extensions typically remain state-specific, optimization-intensive and judged mainly by benchmark energies. This paper shows, in a proof-of-principle study of compact U(1) gauge theory in two spatial dimensions, that a high-quality gauge-equivariant architecture trained only on the ground state can be reused as a generator of structure-resolved spectral data with microscopic details. Combined with correlation-matrix variational analysis, a single learned vacuum yields an excited-state tower that reproduces established low-lying mass-gap benchmarks while exposing operator-resolved structure in both the contractable and winding loop sectors. The winding spectrum reveals finite-width signatures of the flux tube, an emergent reflection quantum number, resolved multi-loop splittings, and a repeated short-distance core excitation alluded earlier as an additional massive scale. More broadly, these results show that learned neural vacua can be used not only to reproduce energies, but also to investigate the structure of the underlying theory with the microscopic information encoded in operator bases. Physical sciences/Physics/Techniques and instrumentation/Design, synthesis and processing Physical sciences/Physics/Particle physics/Theoretical particle physics Physical sciences/Physics/Quantum physics/Quantum mechanics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files supplementinformation.zip Spectroscopy data Cite Share Download PDF Status: Posted 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-9575599","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":634898418,"identity":"17681ca6-aa18-48c1-89b8-3829580a4d46","order_by":0,"name":"Daeho Park","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYDACdiBOMJCQA7EPPCBKCzMQP6iwMQZrSSBWC+ODM2mJDSAOUVr4mbnTJBLbDqfPDzv8EGiLnZxuAwEtks2820BacjfeTjMAakk2NjtAQIvBYZiW2QkgLQcStxGrJd1wdvoHErQknElLkJfOIdIWoF82WyRU2BhukM4pOJBgQIRf+Nl7N978YSAhLz87ffOHDxV2cgS1IFwIVmlArHIQkG8gRfUoGAWjYBSMKAAAbsZGHJL9ElcAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0002-3235-4375","institution":"Yonsei University","correspondingAuthor":true,"prefix":"","firstName":"Daeho","middleName":"","lastName":"Park","suffix":""}],"badges":[],"createdAt":"2026-04-30 10:11:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9575599/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9575599/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109067850,"identity":"230a9b36-3240-4a06-857e-d3f2a7b00926","added_by":"auto","created_at":"2026-05-12 10:01:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4981688,"visible":true,"origin":"","legend":"Article File","description":"","filename":"Neuralspectroscopyrevealsstructurefromalearnedvacuum.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9575599/v1_covered_ffe62ea3-7e9c-434d-8814-9afc87b1fb03.pdf"},{"id":108572698,"identity":"9f6e4f9f-e4cb-47aa-a382-2364d606eb39","added_by":"auto","created_at":"2026-05-06 06:35:29","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":6978048,"visible":true,"origin":"","legend":"Spectroscopy data","description":"","filename":"supplementinformation.zip","url":"https://assets-eu.researchsquare.com/files/rs-9575599/v1/bf91ef41bc9f0baab0c1a8c2.zip"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Neural spectroscopy reveals structure from a learned vacuum","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9575599/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9575599/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Excited states encode the mechanisms of interacting quantum systems and the structure of the underlying theory. 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