{"paper":{"title":"Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Ground states of AKLT models on hexagonal and Lieb lattices satisfy local topological quantum order with exponential boundary decay.","cross_cats":["cond-mat.str-el","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Amanda Young, Bruno Nachtergaele, Thomas Jackson","submitted_at":"2026-05-12T14:27:09Z","abstract_excerpt":"We prove that the ground state of the AKLT models on the hexagonal lattice and the Lieb lattice satisfy the local topological quantum order (LTQO) condition. This will be a consequence of proving that the finite volume ground states are indistinguishable from a unique infinite volume ground state. Concretely, we identify a sequence of increasing and absorbing finite volumes for which any finite volume ground state expectation is well approximated by the infinite volume state with error decaying at a uniform exponential rate in the distance between the support of the observable and boundary of "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The ground states of the AKLT models on the hexagonal lattice and the Lieb lattice satisfy the local topological quantum order (LTQO) condition, with finite-volume ground-state expectations approximating the infinite-volume state at a uniform exponential rate in the distance to the boundary; as a corollary the spectral gap is stable under general small perturbations of sufficient decay.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The polymer representation of the ground state derived by Kennedy, Lieb and Tasaki (1988) admits the necessary modifications to establish the strong form of ground-state indistinguishability required for LTQO on these specific lattices (see abstract and the detailed analysis section referenced therein).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Ground states of AKLT models on hexagonal and Lieb lattices satisfy local topological quantum order with exponential boundary decay.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2984d79f8e375f9d0cd5bbbbd557d212528c742227941866c87b198cde6369f0"},"source":{"id":"2605.12184","kind":"arxiv","version":2},"verdict":{"id":"00c6b2e7-c2b5-40f8-be0f-499f7409cafa","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:41:01.909451Z","strongest_claim":"The ground states of the AKLT models on the hexagonal lattice and the Lieb lattice satisfy the local topological quantum order (LTQO) condition, with finite-volume ground-state expectations approximating the infinite-volume state at a uniform exponential rate in the distance to the boundary; as a corollary the spectral gap is stable under general small perturbations of sufficient decay.","one_line_summary":"Proves LTQO for AKLT models on hexagonal and Lieb lattices by modifying the 1988 polymer representation to obtain uniform exponential decay of boundary effects.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The polymer representation of the ground state derived by Kennedy, Lieb and Tasaki (1988) admits the necessary modifications to establish the strong form of ground-state indistinguishability required for LTQO on these specific lattices (see abstract and the detailed analysis section referenced therein).","pith_extraction_headline":"Ground states of AKLT models on hexagonal and Lieb lattices satisfy local topological quantum order with exponential boundary decay."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.12184/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:01:58.296711Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T10:41:46.932284Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T08:31:17.707274Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T07:50:09.796112Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d91ebdf2ef05388a26b78532ca6f829dd523c541fef2f964f4e6a2357c52f3a6"},"references":{"count":45,"sample":[{"doi":"","year":2020,"title":"H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young. A class of two-dimensional AKLT models with a gap. In A. Young H. Abdul-Rahman, R. Sims, editor,Analytic Trends in Mathematical Physi","work_id":"25a0f023-e71d-4eac-bfab-7c0cfce13c64","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1987,"title":"I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki. Rigorous results on valence-bond ground states in antiferro- magnets.Phys. Rev. Lett., 59:799, 1987","work_id":"c17f9215-6609-42dd-b5b9-c8571df4dcf4","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1988,"title":"I. Affleck, T. Kennedy, E.H. Lieb, and H. Tasaki. Valence bond ground states in isotropic quantum antiferro- magnets.Comm. Math. Phys., 115(3):477–528, 1988","work_id":"cb6c9cb2-503f-4628-8010-4ae85ba6c1da","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1988,"title":"D.P. Arovas, A. Auerbach, and F.D.M. Haldane. 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