{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LTAUBLUOQS6OJVSRUGKPZEC7JK","short_pith_number":"pith:LTAUBLUO","schema_version":"1.0","canonical_sha256":"5cc140ae8e84bce4d651a194fc905f4a8d0292123519624af8a29943e4b01e6f","source":{"kind":"arxiv","id":"1505.06495","version":3},"attestation_state":"computed","paper":{"title":"Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Yuan-Ming Lu","submitted_at":"2015-05-24T22:52:18Z","abstract_excerpt":"Motivated by recent numerical discovery of a gapped spin liquid phase in spin-$1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model, we classify symmetric $Z_2$ spin liquids on triangular lattice in the Abrikosov-fermion representation. We find 20 phases with distinct spinon symmetry quantum numbers, 8 of which have their counterparts in the Schwinger-boson representation. Among them we identify 2 promising candidates (#1 and #20), which can realize a gapped $Z_2$ spin liquid with up to next nearest neighbor mean-field amplitudes. We analyze their neighboring magnetic orders and valence bond s"},"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":"1505.06495","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2015-05-24T22:52:18Z","cross_cats_sorted":[],"title_canon_sha256":"397b41389625bb606f83879a5a34bf4781c40db26ee6236f26042c1781e42e68","abstract_canon_sha256":"8b6a99e78fd701762985d0f4ebef5f77116ae76c47c2b117817ecf78bd67e7ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:12.793616Z","signature_b64":"A5zYc948gACBYhSjfHXxcwpj7rgLVpLgr2PzQRNfgStqBYPCk9NB0MrM+vGaUHF2qaNSBsVsWokLyLNunrfMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc140ae8e84bce4d651a194fc905f4a8d0292123519624af8a29943e4b01e6f","last_reissued_at":"2026-05-18T01:17:12.792909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:12.792909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Yuan-Ming Lu","submitted_at":"2015-05-24T22:52:18Z","abstract_excerpt":"Motivated by recent numerical discovery of a gapped spin liquid phase in spin-$1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model, we classify symmetric $Z_2$ spin liquids on triangular lattice in the Abrikosov-fermion representation. We find 20 phases with distinct spinon symmetry quantum numbers, 8 of which have their counterparts in the Schwinger-boson representation. Among them we identify 2 promising candidates (#1 and #20), which can realize a gapped $Z_2$ spin liquid with up to next nearest neighbor mean-field amplitudes. We analyze their neighboring magnetic orders and valence bond s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06495","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":"1505.06495","created_at":"2026-05-18T01:17:12.793033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06495v3","created_at":"2026-05-18T01:17:12.793033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06495","created_at":"2026-05-18T01:17:12.793033+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTAUBLUOQS6O","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTAUBLUOQS6OJVSR","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTAUBLUO","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2512.23962","citing_title":"Lectures on insulating and conducting quantum spin liquids","ref_index":32,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK","json":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK.json","graph_json":"https://pith.science/api/pith-number/LTAUBLUOQS6OJVSRUGKPZEC7JK/graph.json","events_json":"https://pith.science/api/pith-number/LTAUBLUOQS6OJVSRUGKPZEC7JK/events.json","paper":"https://pith.science/paper/LTAUBLUO"},"agent_actions":{"view_html":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK","download_json":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK.json","view_paper":"https://pith.science/paper/LTAUBLUO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06495&json=true","fetch_graph":"https://pith.science/api/pith-number/LTAUBLUOQS6OJVSRUGKPZEC7JK/graph.json","fetch_events":"https://pith.science/api/pith-number/LTAUBLUOQS6OJVSRUGKPZEC7JK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK/action/storage_attestation","attest_author":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK/action/author_attestation","sign_citation":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK/action/citation_signature","submit_replication":"https://pith.science/pith/LTAUBLUOQS6OJVSRUGKPZEC7JK/action/replication_record"}},"created_at":"2026-05-18T01:17:12.793033+00:00","updated_at":"2026-05-18T01:17:12.793033+00:00"}