{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IB4TE476VHYX36PTXUDDVGVI5T","short_pith_number":"pith:IB4TE476","schema_version":"1.0","canonical_sha256":"40793273fea9f17df9f3bd063a9aa8ecde9f6dce099b22f84018cf39d54c412e","source":{"kind":"arxiv","id":"1403.2035","version":3},"attestation_state":"computed","paper":{"title":"Quantum distance and the Euler number index of the Bloch band in a 1D spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Yu-Quan Ma","submitted_at":"2014-03-09T07:51:05Z","abstract_excerpt":"We study the Riemannian metric and the Euler characteristic number of the Bloch band in a 1D spin model with multi-site spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions"},"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":"1403.2035","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2014-03-09T07:51:05Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"26b94d4d31db8adcbef8dbfade4a26969676550b87790765ce06de602810913b","abstract_canon_sha256":"d9b848f5e549ed06e5ce5db3d792345bdd0ec8129be4fe4e7bd70fc069fe3442"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:31.982005Z","signature_b64":"cC96IMssiEyaPS3OVA2vpM60SPgPMTl0SWgrqdnckhLAXAfB1SIWZ6E5A85424O/0PmmuIuecqJUMIejZEGTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40793273fea9f17df9f3bd063a9aa8ecde9f6dce099b22f84018cf39d54c412e","last_reissued_at":"2026-05-18T02:39:31.981540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:31.981540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum distance and the Euler number index of the Bloch band in a 1D spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Yu-Quan Ma","submitted_at":"2014-03-09T07:51:05Z","abstract_excerpt":"We study the Riemannian metric and the Euler characteristic number of the Bloch band in a 1D spin model with multi-site spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2035","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1403.2035","created_at":"2026-05-18T02:39:31.981613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.2035v3","created_at":"2026-05-18T02:39:31.981613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2035","created_at":"2026-05-18T02:39:31.981613+00:00"},{"alias_kind":"pith_short_12","alias_value":"IB4TE476VHYX","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IB4TE476VHYX36PT","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IB4TE476","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T","json":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T.json","graph_json":"https://pith.science/api/pith-number/IB4TE476VHYX36PTXUDDVGVI5T/graph.json","events_json":"https://pith.science/api/pith-number/IB4TE476VHYX36PTXUDDVGVI5T/events.json","paper":"https://pith.science/paper/IB4TE476"},"agent_actions":{"view_html":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T","download_json":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T.json","view_paper":"https://pith.science/paper/IB4TE476","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.2035&json=true","fetch_graph":"https://pith.science/api/pith-number/IB4TE476VHYX36PTXUDDVGVI5T/graph.json","fetch_events":"https://pith.science/api/pith-number/IB4TE476VHYX36PTXUDDVGVI5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T/action/storage_attestation","attest_author":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T/action/author_attestation","sign_citation":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T/action/citation_signature","submit_replication":"https://pith.science/pith/IB4TE476VHYX36PTXUDDVGVI5T/action/replication_record"}},"created_at":"2026-05-18T02:39:31.981613+00:00","updated_at":"2026-05-18T02:39:31.981613+00:00"}