{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:P2M6A2DWYBPYBBYAC45ZEUGES5","short_pith_number":"pith:P2M6A2DW","schema_version":"1.0","canonical_sha256":"7e99e06876c05f808700173b9250c49753cca42f535767f573ae1f9004d52bf6","source":{"kind":"arxiv","id":"1606.00334","version":3},"attestation_state":"computed","paper":{"title":"Symmetry fractionalization in the topological phase of the spin-$\\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"I. P. McCulloch, S. N. Saadatmand","submitted_at":"2016-06-01T15:59:09Z","abstract_excerpt":"Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$\\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the triangular lattice. We find four distinct ground-states characteristic of a non-chiral, $Z_2$ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to coexistence of symmetry protected a"},"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":"1606.00334","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-06-01T15:59:09Z","cross_cats_sorted":[],"title_canon_sha256":"968b4e83f156907ba0fb840b8542cab598a5f6494903e934b8db4029d02267ea","abstract_canon_sha256":"fcaaed53acbfca27869148d7f5894d6b825b0dc440775c42b2f9d77d68d9a8fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:41.735326Z","signature_b64":"WVLIKOJI3KnSiDmxc/yfL4hZaXtE2xKjsZk1pPupYrDdJcHLeN8s+8v+1HcwL4qRs0YE74/HGJdktljRMQbjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e99e06876c05f808700173b9250c49753cca42f535767f573ae1f9004d52bf6","last_reissued_at":"2026-05-18T00:18:41.734620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:41.734620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetry fractionalization in the topological phase of the spin-$\\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"I. P. McCulloch, S. N. Saadatmand","submitted_at":"2016-06-01T15:59:09Z","abstract_excerpt":"Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$\\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the triangular lattice. We find four distinct ground-states characteristic of a non-chiral, $Z_2$ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to coexistence of symmetry protected a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00334","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":"1606.00334","created_at":"2026-05-18T00:18:41.734723+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00334v3","created_at":"2026-05-18T00:18:41.734723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00334","created_at":"2026-05-18T00:18:41.734723+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2M6A2DWYBPY","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2M6A2DWYBPYBBYA","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2M6A2DW","created_at":"2026-05-18T12:30:36.002864+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/P2M6A2DWYBPYBBYAC45ZEUGES5","json":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5.json","graph_json":"https://pith.science/api/pith-number/P2M6A2DWYBPYBBYAC45ZEUGES5/graph.json","events_json":"https://pith.science/api/pith-number/P2M6A2DWYBPYBBYAC45ZEUGES5/events.json","paper":"https://pith.science/paper/P2M6A2DW"},"agent_actions":{"view_html":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5","download_json":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5.json","view_paper":"https://pith.science/paper/P2M6A2DW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00334&json=true","fetch_graph":"https://pith.science/api/pith-number/P2M6A2DWYBPYBBYAC45ZEUGES5/graph.json","fetch_events":"https://pith.science/api/pith-number/P2M6A2DWYBPYBBYAC45ZEUGES5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5/action/storage_attestation","attest_author":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5/action/author_attestation","sign_citation":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5/action/citation_signature","submit_replication":"https://pith.science/pith/P2M6A2DWYBPYBBYAC45ZEUGES5/action/replication_record"}},"created_at":"2026-05-18T00:18:41.734723+00:00","updated_at":"2026-05-18T00:18:41.734723+00:00"}