Out of Time Order Correlators as Measures of Quantum Information Scrambling with Spectral Diagnostic

Out of Time Order Correlators as Measures of Quantum Information Scrambling with Spectral Diagnostic | 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 Research Article Out of Time Order Correlators as Measures of Quantum Information Scrambling with Spectral Diagnostic Bannishikha Banerjee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9329643/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Out-of-time-order correlators (OTOCs) have emerged as the preeminent theoretical and experimental probe of quantum information scrambling — the delocalization of quantum information across many-body degrees of freedom. Here we present a comprehensive computational study of OTOCs across three paradigmatic models: the Sachdev-Ye-Kitaev (SYK) model, the non-integrable transverse-field Ising chain, and random unitary circuits. Through exact diagonalization and large-N analytics, we extract Lyapunov exponents, scrambling times, and butterfly velocities, demonstrating that all chaotic systems studied approach, but do not saturate, the Maldacena-Shenker-Stanford (MSS) bound λ_L ≤ 2π/β. Crucially, we introduce the Spectral Out-of-Time-Order Correlator (SOTOC), a novel frequency-domain diagnostic that decomposes information scrambling into its constituent spectral modes. The SOTOC achieves a 32% improvement in Lyapunov exponent extraction precision over conventional log-linear fitting and maintains robust performance at noise levels σ > 0.30, where traditional methods fail. Our phase diagram reveals a sharp transition in scrambling dynamics at h/J ≈ 1.0 in the TFIM, coinciding with the onset of quantum chaos as measured by level-spacing statistics. These results establish SOTOC as a practical and theoretically grounded tool for probing scrambling in near-term quantum devices and holographic systems. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 02 May, 2026 Reviewers agreed at journal 28 Apr, 2026 Reviewers invited by journal 27 Apr, 2026 Editor assigned by journal 27 Apr, 2026 Editor invited by journal 27 Apr, 2026 Submission checks completed at journal 20 Apr, 2026 First submitted to journal 20 Apr, 2026 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. 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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-9329643","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":633414437,"identity":"8f9ba8af-69c5-41e7-99b5-e51d79123b4b","order_by":0,"name":"Bannishikha Banerjee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACAxCR2ABmJzAwVAApZuYGUrScAWlhJEILXA1jGwoXOzBnP3vswcMddnn80gcePvg4rzaavx2o5UfFNpxaLHvy0g0SzyQXS/YlJBvO3HY8d8ZhxgbGnjO3cTvsQI6ZRGIbc+KGMwxp0rzbjuU2ALUwM7bh0XL+DUhLfeL+Mwzpv//OOZY7n6CWG2BbDidu4GFIA4ZVTe4GQlosZ4BsOXM8ccYZhmTJnmMHcjcCtRzE5xdz/hwzyZ87qhP7e3gSP/yoqcudd/7wwQc/KnBrQQI8CUDiMJh5gBj1QMAOUlhHpOJRMApGwSgYSQAAGSVgTqRG/TsAAAAASUVORK5CYII=","orcid":"","institution":"Amity University","correspondingAuthor":true,"prefix":"","firstName":"Bannishikha","middleName":"","lastName":"Banerjee","suffix":""}],"badges":[],"createdAt":"2026-04-06 04:23:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9329643/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9329643/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108805580,"identity":"f48d84a2-48d5-4b07-88fa-b7bb7add4e5f","added_by":"auto","created_at":"2026-05-08 15:26:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":779650,"visible":true,"origin":"","legend":"","description":"","filename":"OTOCPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9329643/v1_covered_c66f81ca-3b06-4891-a144-96ca951ae6aa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Out of Time Order Correlators as Measures of Quantum Information Scrambling with Spectral Diagnostic","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"discover-quantum-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Quantum Science](https://link.springer.com/journal/44464)","snPcode":"44464","submissionUrl":"https://submission.nature.com/new-submission/44464/3","title":"Discover Quantum Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9329643/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9329643/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOut-of-time-order correlators (OTOCs) have emerged as the preeminent theoretical and experimental probe of quantum information scrambling \u0026mdash; the delocalization of quantum information across many-body degrees of freedom. 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