{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:F7WQOXSRFEPOCL5CZUIW3LPQMA","short_pith_number":"pith:F7WQOXSR","schema_version":"1.0","canonical_sha256":"2fed075e51291ee12fa2cd116dadf06027303d1ebf85deaa3be1220b3b526e97","source":{"kind":"arxiv","id":"1611.06093","version":3},"attestation_state":"computed","paper":{"title":"Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Andreas R\\\"uegg, Manfred Sigrist, Markus Legner, Wei Chen","submitted_at":"2016-11-18T14:22:49Z","abstract_excerpt":"The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows to extract a correlation length that diverges at topological phase transitions. The correlation len"},"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":"1611.06093","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-11-18T14:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"ab0d894ed735d00ec753af107a0ddffdb2b2b8e5dd77e910327105949d4966a1","abstract_canon_sha256":"1122c34d1028bf4b2da4d507bbd2bd382a02a6ce1fb4c693169d528e5f2068a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:13.048475Z","signature_b64":"PRyXj5zkCIpV8PrJ2CygEjjkvwDYCHyrBQFGhHU+l6tjd/5gumTIUSX1yEk+JxACKXtL9005bNcXh419QvreCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fed075e51291ee12fa2cd116dadf06027303d1ebf85deaa3be1220b3b526e97","last_reissued_at":"2026-05-18T00:51:13.047765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:13.047765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Andreas R\\\"uegg, Manfred Sigrist, Markus Legner, Wei Chen","submitted_at":"2016-11-18T14:22:49Z","abstract_excerpt":"The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows to extract a correlation length that diverges at topological phase transitions. The correlation len"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06093","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":"1611.06093","created_at":"2026-05-18T00:51:13.047869+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06093v3","created_at":"2026-05-18T00:51:13.047869+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06093","created_at":"2026-05-18T00:51:13.047869+00:00"},{"alias_kind":"pith_short_12","alias_value":"F7WQOXSRFEPO","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"F7WQOXSRFEPOCL5C","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"F7WQOXSR","created_at":"2026-05-18T12:30:15.759754+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/F7WQOXSRFEPOCL5CZUIW3LPQMA","json":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA.json","graph_json":"https://pith.science/api/pith-number/F7WQOXSRFEPOCL5CZUIW3LPQMA/graph.json","events_json":"https://pith.science/api/pith-number/F7WQOXSRFEPOCL5CZUIW3LPQMA/events.json","paper":"https://pith.science/paper/F7WQOXSR"},"agent_actions":{"view_html":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA","download_json":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA.json","view_paper":"https://pith.science/paper/F7WQOXSR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06093&json=true","fetch_graph":"https://pith.science/api/pith-number/F7WQOXSRFEPOCL5CZUIW3LPQMA/graph.json","fetch_events":"https://pith.science/api/pith-number/F7WQOXSRFEPOCL5CZUIW3LPQMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA/action/storage_attestation","attest_author":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA/action/author_attestation","sign_citation":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA/action/citation_signature","submit_replication":"https://pith.science/pith/F7WQOXSRFEPOCL5CZUIW3LPQMA/action/replication_record"}},"created_at":"2026-05-18T00:51:13.047869+00:00","updated_at":"2026-05-18T00:51:13.047869+00:00"}