{"paper":{"title":"Lattice non-invertible symmetry from non-commuting transfer matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Eric Vernier, Masahito Yamazaki, Yuan Miao","submitted_at":"2026-06-24T10:12:44Z","abstract_excerpt":"We establish a direct connection between Onsager symmetry, duality defects, and quantum integrability in the XXZ spin chain at roots of unity, $\\Delta=(q+q^{-1})/2$ with $q^N=\\pm1$. Using a non-Abelian algebra of transfer matrices governed by an unbalanced version of the Yang--Baxter/RLL relation, we construct an explicit lattice realization of the Onsager algebra and its duality automorphism. The duality is represented by a matrix product operator related to the transfer matrices of the $\\tau_2$ model. We show that this operator obeys $\\mathbb{Z}_N$ Tambara--Yamagami fusion rules and therefor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25660","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25660/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}