{"paper":{"title":"Strict area law implies commuting parent Hamiltonian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Bowen Shi, Daniel Ranard, Isaac H. Kim, Ting-Chun Lin","submitted_at":"2024-04-08T21:01:49Z","abstract_excerpt":"We show that in two spatial dimensions, when a quantum state has entanglement entropy obeying a strict area law, meaning $S(A)=\\alpha |\\partial A| - \\gamma$ for constants $\\alpha, \\gamma$ independent of lattice region $A$, then it admits a commuting parent Hamiltonian. More generally, we prove that the entanglement bootstrap axioms in 2D imply the existence of a commuting, local parent Hamiltonian with a stable spectral gap. We also extend our proof to states that describe gapped domain walls. Physically, these results imply that the states studied in the entanglement bootstrap program corresp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.05867","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/2404.05867/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"}