Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction

[2501.15506] Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Statistical Mechanics arXiv:2501.15506 (cond-mat) [Submitted on 26 Jan 2025 ( v1 ), last revised 10 Apr 2026 (this version, v3)] Title: Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction Authors: Naoto Shiraishi View a PDF of the paper titled Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction, by Naoto Shiraishi View PDF HTML (experimental) Abstract: We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities. Comments: 72 pages, no figure Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph) Cite as: arXiv:2501.15506 [cond-mat.stat-mech] (or arXiv:2501.15506v3 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2501.15506 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Stat. Phys. 192, 170 (2025) Related DOI : https://doi.org/10.1007/s10955-025-03551-5 Focus to learn more DOI(s) linking to related resources Submission history From: Naoto Shiraishi [ view email ] [v1] Sun, 26 Jan 2025 12:48:19 UTC (54 KB) [v2] Wed, 19 Mar 2025 12:23:22 UTC (55 KB) [v3] Fri, 10 Apr 2026 12:56:55 UTC (69 KB) Full-text links: Access Paper: View a PDF of the paper titled Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction, by Naoto Shiraishi View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2025-01 Change to browse by: cond-mat cond-mat.str-el math math-ph math.MP quant-ph References & Citations INSPIRE HEP NASA ADS Google 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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