Experimental observation of exact quantum critical states

Experimental observation of exact quantum critical states | 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 Experimental observation of exact quantum critical states Xiong-Jun Liu, Wenhui Huang, Xin-Chi Zhou, Libo Zhang, Jiawei Zhang, and 27 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6697488/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 Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical. Confirming the presence of critical states necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple spin qubit system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges. Physical sciences/Physics/Quantum physics/Quantum simulation Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Full Text Additional Declarations There is NO Competing Interest. Supplementary Files supplement.pdf Supplementary information for ''Experimental observation of exact quantum critical states'' 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-6697488","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":466537366,"identity":"af6b7e10-06d5-4262-b7eb-f7c3679415e5","order_by":0,"name":"Xiong-Jun 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Confirming the presence of critical states necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple spin qubit system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges.","manuscriptTitle":"Experimental observation of exact quantum critical states","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-30 08:54:36","doi":"10.21203/rs.3.rs-6697488/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-physics","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"nphys","sideBox":"Learn more about [Nature Physics](http://www.nature.com/nphys/)","snPcode":"","submissionUrl":"","title":"Nature Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Research","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"b183de29-f35b-41c3-ae89-8ac0c6037736","owner":[],"postedDate":"July 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":49533992,"name":"Physical sciences/Physics/Quantum physics/Quantum simulation"},{"id":49533993,"name":"Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena"},{"id":49533994,"name":"Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2025-07-30T08:54:36+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-30 08:54:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6697488","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6697488","identity":"rs-6697488","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}