{"paper":{"title":"Translation symmetry-enforced long-range entanglement in mixed states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The fixed-point state of strong-to-weak translation symmetry breaking is long-range entangled and cannot be a mixture of short-range entangled states.","cross_cats":["cond-mat.mes-hall","cond-mat.str-el","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Carolyn Zhang, Lei Gioia, Ryan Thorngren","submitted_at":"2026-05-14T17:59:57Z","abstract_excerpt":"We show by a counting argument that even though translation symmetry admits symmetric short-range entangled (SRE) eigenstates, there are not enough such SRE eigenstates to span the zero momentum sector. This means that the fixed point strong-to-weak spontaneous symmetry breaking state of translation symmetry is long-range entangled: it cannot be written as a mixture of SRE states. This is a subtle form of long-range entanglement in mixed states that cannot be detected by long-range connected correlation functions."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the fixed point strong-to-weak spontaneous symmetry breaking state of translation symmetry is long-range entangled: it cannot be written as a mixture of SRE states.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the counting argument correctly establishes an insufficient number of symmetric short-range entangled eigenstates to span the zero-momentum sector, relying on precise definitions of SRE states and the structure of the Hilbert space under translation symmetry.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A counting argument proves that the fixed-point strong-to-weak spontaneous symmetry breaking state under translation symmetry is long-range entangled because symmetric short-range entangled states are insufficient to span the zero-momentum sector.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The fixed-point state of strong-to-weak translation symmetry breaking is long-range entangled and cannot be a mixture of short-range entangled states.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"eb714456ebb6aa19138c8cfd3def59f9318b3ada3f8377685f73af94993e1179"},"source":{"id":"2605.15200","kind":"arxiv","version":1},"verdict":{"id":"3f6b8c16-37e0-4b10-8cd9-423f5ad0c40b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:08:17.003946Z","strongest_claim":"the fixed point strong-to-weak spontaneous symmetry breaking state of translation symmetry is long-range entangled: it cannot be written as a mixture of SRE states.","one_line_summary":"A counting argument proves that the fixed-point strong-to-weak spontaneous symmetry breaking state under translation symmetry is long-range entangled because symmetric short-range entangled states are insufficient to span the zero-momentum sector.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the counting argument correctly establishes an insufficient number of symmetric short-range entangled eigenstates to span the zero-momentum sector, relying on precise definitions of SRE states and the structure of the Hilbert space under translation symmetry.","pith_extraction_headline":"The fixed-point state of strong-to-weak translation symmetry breaking is long-range entangled and cannot be a mixture of short-range entangled states."},"references":{"count":28,"sample":[{"doi":"","year":2011,"title":"M. B. Hastings, Phys. Rev. Lett.107, 210501 (2011)","work_id":"d47b2abd-dba9-4d8e-b9f3-98bd0ff27c25","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Y .-H. Chen and T. Grover, Phys. Rev. Lett.132, 170602 (2024)","work_id":"9856bbac-c5bc-41b6-a971-f790e3362e2d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Y .-H. Chen and T. Grover, PRX Quantum5, 030310 (2024)","work_id":"b60f1aad-6898-4567-a801-bafc05107789","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"C. de Groot, A. Turzillo, and N. Schuch, Quantum6, 856 (2022)","work_id":"1cbf7045-12c5-4570-9b3d-dcb2123b4cdd","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"A. Moharramipour, L. A. Lessa, C. Wang, T. H. Hsieh, and S. Sahu, PRX Quantum5, 040336 (2024)","work_id":"319731a5-196e-4056-8ea8-26f4120c5c19","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"786b5d64110fa89a5bfc9833e7de6314062a9dd478991a25d29e4c39f45797fa","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"}