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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 ","authors_text":"Amanda Young, Bruno Nachtergaele, Thomas Jackson","cross_cats":["cond-mat.str-el","math.MP","quant-ph"],"headline":"Ground states of AKLT models on hexagonal and Lieb lattices satisfy local topological quantum order with exponential boundary decay.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-12T14:27:09Z","title":"Local Topological Quantum Order and Spectral Gap Stability for the AKLT Models on the Hexagonal and Lieb Lattices"},"references":{"count":45,"internal_anchors":2,"resolved_work":45,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"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","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"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","year":1987},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"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","year":1988},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"D.P. Arovas, A. Auerbach, and F.D.M. Haldane. Extended heisenberg models of antiferromagnetism: Analogies to the fractional quantum hall effect.Phys. Rev. Lett., 60:531–534, 1988","work_id":"1e039ad7-9fd1-4f4e-949f-c3e386377c41","year":1988},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"S. Bachmann, E. Hamza, B. Nachtergaele, and A. Young. Product Vacua and Boundary State models ind dimensions.J. Stat. Phys., 160:636–658, 2015","work_id":"12d660ea-bd15-486c-a23e-7dac41791dcf","year":2015}],"snapshot_sha256":"aef4c540edbab4efe7e0fc1dd99613b454531dd47f22f42d708e3bab2a5225a3"},"source":{"id":"2605.12184","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-19T17:41:01.909451Z","id":"00c6b2e7-c2b5-40f8-be0f-499f7409cafa","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Ground states of AKLT models on hexagonal and Lieb lattices satisfy local topological quantum order with exponential boundary decay.","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.","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)."}},"verdict_id":"00c6b2e7-c2b5-40f8-be0f-499f7409cafa"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4f9560e49365636fbb5a1781b44b2bb0ae5a1c0b0be70615bbfd7bcc32d614ae","target":"record","created_at":"2026-05-20T00:01:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7684bfb7c9ea098015868fb67de391bdbd6de819a6fa7e5156ee1324a2b86bfc","cross_cats_sorted":["cond-mat.str-el","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-12T14:27:09Z","title_canon_sha256":"3024a3a2f5a0c7fc581e0192563a4887b2dc20766c65db7185c54d565be5da87"},"schema_version":"1.0","source":{"id":"2605.12184","kind":"arxiv","version":2}},"canonical_sha256":"0c414f1f267a780ed5329ec9cd371db4b5677d748f41834addec046cc340b1a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c414f1f267a780ed5329ec9cd371db4b5677d748f41834addec046cc340b1a8","first_computed_at":"2026-05-20T00:01:43.957353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:43.957353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S/lK2Az0Mfjh3yt4A5bKLj1h6fYhdmQsE7B8VGb5SX91qpqIn0cVcd4bcwy5z94ypVlQptjMVkKZwPC3SntTCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:43.958244Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.12184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f9560e49365636fbb5a1781b44b2bb0ae5a1c0b0be70615bbfd7bcc32d614ae","sha256:5e6e026974c4109b7a545ee7fc7b1ae1a1362878c70c4b21a0e69189033e0603"],"state_sha256":"92cfbb19ef2b8f3dee3284ab2700ba9907294e777489c79529efbe7c237aa181"}