Exact strong zero modes are generic in integrable spin systems with large anisotropy
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Quantum Physics arXiv:2605.26205 (quant-ph) [Submitted on 25 May 2026] Title:Exact strong zero modes are generic in integrable spin systems with large anisotropy Authors:Sascha Gehrmann View a PDF of the paper titled Exact strong zero modes are generic in integrable spin systems with large anisotropy, by Sascha Gehrmann View PDF Abstract:Strong zero modes (SZMs) are edge-localized operators that commute with the Hamiltonian up to corrections exponentially small in system size, yielding anomalously long edge coherence times. In some settings, notably certain integrable models, this commutator can be made to vanish exactly at finite size, defining an exact SZM (ESZM). Existing ESZM constructions in the integrable setting, however, have proceeded model by model and have not been unified into a common framework. Here, I show that ESZMs arise generically in a broad family of integrable spin models with anisotropic interactions. Their existence follows from two algebraic properties of the underlying R- and K-matrices -- quasi-periodicity in the spectral parameter and tracelessness, respectively -- providing a uniform, model-independent mechanism. The framework recovers the known ESZM in XXZ chain and its higher-spin generalizations as special cases and predicts ESZMs in previously unrecognized models. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2605.26205 [quant-ph] (or arXiv:2605.26205v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.26205 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sascha Gehrmann [view email] [v1] Mon, 25 May 2026 18:00:00 UTC (3,178 KB) Full-text links: Access Paper: View a PDF of the paper titled Exact strong zero modes are generic in integrable spin systems with large anisotropy, by Sascha GehrmannView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.stat-mech 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?)