Isospectrality and Operator Complexity
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Quantum Physics arXiv:2606.05294 (quant-ph) [Submitted on 3 Jun 2026] Title:Isospectrality and Operator Complexity Authors:Pradip Kattel, Yicheng Tang, Natan Andrei View a PDF of the paper titled Isospectrality and Operator Complexity, by Pradip Kattel and 2 other authors View PDF HTML (experimental) Abstract:We study a pair of exactly solvable, isospectral fermion chains, one strongly interacting and one quadratic, that nevertheless display remarkably different phase structures and operator dynamics. A nonlocal nonlinear unitary transformation maps one onto the other while preserving the entire many-body spectrum and converting local fermion operators into extended many-body strings. Thus, operators that evolve within a closed linear subspace in the quadratic model become interacting operators that generate increasingly higher-body terms and exhibit asymptotic Lanczos growth $b_n\propto\sqrt n$. Despite their identical spectra, the two models realize distinct phases and sharply different notions of operator complexity. Our results demonstrate that free many-body spectra and interacting operator dynamics are fundamentally compatible. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con); Mathematical Physics (math-ph) Cite as: arXiv:2606.05294 [quant-ph] (or arXiv:2606.05294v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.05294 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pradip Kattel [view email] [v1] Wed, 3 Jun 2026 18:00:05 UTC (309 KB) Full-text links: Access Paper: View a PDF of the paper titled Isospectrality and Operator Complexity, by Pradip Kattel and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el cond-mat.supr-con math math-ph math.MP 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?) 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?)