{"paper":{"title":"Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander F. Kemper, Bojko N. Bakalov, Efekan K\\\"okc\\\"u, Roeland Wiersema","submitted_at":"2023-09-11T17:59:41Z","abstract_excerpt":"Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by translation-invariant 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras. We consider chains with open and periodic boundary conditions and find 17 unique dynamical Lie algebras. Our classification covers some well-known models such as the transverse-field Ising model and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05690","kind":"arxiv","version":2},"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/2309.05690/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"}