{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:3543VY3LQACMTQGJ6TDWM3PICI","short_pith_number":"pith:3543VY3L","schema_version":"1.0","canonical_sha256":"df79bae36b8004c9c0c9f4c7666de81230de377636febb55ab636964d4a6fb49","source":{"kind":"arxiv","id":"2112.06946","version":2},"attestation_state":"computed","paper":{"title":"Non-zero momentum requires long-range entanglement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Chong Wang, Lei Gioia","submitted_at":"2021-12-13T19:00:04Z","abstract_excerpt":"We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue $e^{iP}\\neq1$. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. Some non-trivial consequences follow immediately from our theorem: (1) several different types of Lieb-Schultz-Mattis-Oshikawa-Hastings (LSMOH) theorems, including"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2112.06946","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.str-el","submitted_at":"2021-12-13T19:00:04Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th","quant-ph"],"title_canon_sha256":"28d3d0f6c83dc70888dc4569b035fc0706206c127fc57722972b8d5429f2fc56","abstract_canon_sha256":"46e0bfdd408b371acee7b724fad2f1d72f63f546a8583026424c06f3b7e38fd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:40:24.975672Z","signature_b64":"Wctifnpquv71mdevVcM9zmN49o6nNXlIfBV3qIOte5wIsl1srpeeKMMQppGEWlLdDpGUevyT0YdI7FQgv4RxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df79bae36b8004c9c0c9f4c7666de81230de377636febb55ab636964d4a6fb49","last_reissued_at":"2026-07-05T04:40:24.975161Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:40:24.975161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-zero momentum requires long-range entanglement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Chong Wang, Lei Gioia","submitted_at":"2021-12-13T19:00:04Z","abstract_excerpt":"We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue $e^{iP}\\neq1$. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. Some non-trivial consequences follow immediately from our theorem: (1) several different types of Lieb-Schultz-Mattis-Oshikawa-Hastings (LSMOH) theorems, including"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06946","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/2112.06946/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2112.06946","created_at":"2026-07-05T04:40:24.975218+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.06946v2","created_at":"2026-07-05T04:40:24.975218+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06946","created_at":"2026-07-05T04:40:24.975218+00:00"},{"alias_kind":"pith_short_12","alias_value":"3543VY3LQACM","created_at":"2026-07-05T04:40:24.975218+00:00"},{"alias_kind":"pith_short_16","alias_value":"3543VY3LQACMTQGJ","created_at":"2026-07-05T04:40:24.975218+00:00"},{"alias_kind":"pith_short_8","alias_value":"3543VY3L","created_at":"2026-07-05T04:40:24.975218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2601.01191","citing_title":"Tori, Klein Bottles, and Modulo 8 Parity/Time-reversal Anomalies of 2+1d Staggered Fermions","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI","json":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI.json","graph_json":"https://pith.science/api/pith-number/3543VY3LQACMTQGJ6TDWM3PICI/graph.json","events_json":"https://pith.science/api/pith-number/3543VY3LQACMTQGJ6TDWM3PICI/events.json","paper":"https://pith.science/paper/3543VY3L"},"agent_actions":{"view_html":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI","download_json":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI.json","view_paper":"https://pith.science/paper/3543VY3L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.06946&json=true","fetch_graph":"https://pith.science/api/pith-number/3543VY3LQACMTQGJ6TDWM3PICI/graph.json","fetch_events":"https://pith.science/api/pith-number/3543VY3LQACMTQGJ6TDWM3PICI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI/action/storage_attestation","attest_author":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI/action/author_attestation","sign_citation":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI/action/citation_signature","submit_replication":"https://pith.science/pith/3543VY3LQACMTQGJ6TDWM3PICI/action/replication_record"}},"created_at":"2026-07-05T04:40:24.975218+00:00","updated_at":"2026-07-05T04:40:24.975218+00:00"}