Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures
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Quantum Physics arXiv:2602.11278 (quant-ph) [Submitted on 11 Feb 2026] Title:Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures Authors:Rishabh Jha, Heiko Georg Menzler View a PDF of the paper titled Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures, by Rishabh Jha and 1 other authors View PDF HTML (experimental) Abstract:Krylov subspace methods quantify operator growth in quantum many-body systems through Lanczos coefficients that encode how operators spread under time evolution. While these diagnostics have been proposed to distinguish quantum chaos from integrability, quadratic fermionic Hamiltonians are widely expected to exhibit trivial Lanczos structure. Here we demonstrate that Lanczos coefficients generated from local boundary operators provide a quantitative diagnostic of whether the lowest excitation gap is controlled by boundary-localized or bulk-extended modes in the long-range Kitaev chain, the model for topological superconductivity with algebraically decaying couplings. We introduce \emph{Krylov staggering parameter}, defined as the logarithmic ratio of consecutive odd and even Lanczos coefficients, whose sign structure correlates robustly with the edge versus bulk character of the gap across the full phase diagram. This correlation arises from a bipartite Krylov structure induced by pairing, power-law couplings, and open boundaries. We derive an exact single-particle operator Lanczos algorithm that reduces the recursion from exponentially large operator space to a finite-dimensional linear problem, achieving machine precision for chains of hundreds of sites. These results establish Krylov diagnostics as operational probes of how low-energy excitations are localized along the chain and how strongly they are tied to the boundaries with broken U(1) symmetry, with potential applications to trapped-ion and cold-atom quantum simulators. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2602.11278 [quant-ph] (or arXiv:2602.11278v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.11278 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rishabh Jha [view email] [v1] Wed, 11 Feb 2026 19:00:05 UTC (4,583 KB) Full-text links: Access Paper: View a PDF of the paper titled Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures, by Rishabh Jha and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)