{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:W2BTC4SVRSFQECKEPGZHAS7QYA","short_pith_number":"pith:W2BTC4SV","schema_version":"1.0","canonical_sha256":"b6833172558c8b02094479b2704bf0c02c92fe59f1e85090c8ae897a97523ded","source":{"kind":"arxiv","id":"1804.04337","version":5},"attestation_state":"computed","paper":{"title":"Topological phase transition and $\\mathbb{Z}_2$ index for $S=1$ quantum spin chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hal Tasaki","submitted_at":"2018-04-12T06:15:35Z","abstract_excerpt":"We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is invariant under smooth deformation. By using the index, we provide the first rigorous proof of the existence of a \"topological\" phase transition, which cannot be characterized by any conventional order parameters, between the AKLT ground state and trivial ground states. This rigorously establishes that the AKLT model is in a nontrivial symmetry protected topological"},"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":"1804.04337","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-04-12T06:15:35Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"00fc15beb5cd0d757c803f34f651a746ebacb3a96ddfb01f9016944d2ade47c2","abstract_canon_sha256":"d721cd3e94793e72f57f7eb8746cc2cd956e17709f3414089f32132a49f83948"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:49.151416Z","signature_b64":"m1kSOb5JlAIDQUMQ3YX/BLoawdztPf4MWZut6iNOi6vIPHrYbyWfRcR+Ine0Bk+0TdIoiRradC9xlHWrNp0wBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6833172558c8b02094479b2704bf0c02c92fe59f1e85090c8ae897a97523ded","last_reissued_at":"2026-05-18T00:03:49.150857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:49.150857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological phase transition and $\\mathbb{Z}_2$ index for $S=1$ quantum spin chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hal Tasaki","submitted_at":"2018-04-12T06:15:35Z","abstract_excerpt":"We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is invariant under smooth deformation. By using the index, we provide the first rigorous proof of the existence of a \"topological\" phase transition, which cannot be characterized by any conventional order parameters, between the AKLT ground state and trivial ground states. This rigorously establishes that the AKLT model is in a nontrivial symmetry protected topological"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04337","kind":"arxiv","version":5},"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":"1804.04337","created_at":"2026-05-18T00:03:49.150941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.04337v5","created_at":"2026-05-18T00:03:49.150941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04337","created_at":"2026-05-18T00:03:49.150941+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2BTC4SVRSFQ","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2BTC4SVRSFQECKE","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2BTC4SV","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2407.17041","citing_title":"The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA","json":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA.json","graph_json":"https://pith.science/api/pith-number/W2BTC4SVRSFQECKEPGZHAS7QYA/graph.json","events_json":"https://pith.science/api/pith-number/W2BTC4SVRSFQECKEPGZHAS7QYA/events.json","paper":"https://pith.science/paper/W2BTC4SV"},"agent_actions":{"view_html":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA","download_json":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA.json","view_paper":"https://pith.science/paper/W2BTC4SV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.04337&json=true","fetch_graph":"https://pith.science/api/pith-number/W2BTC4SVRSFQECKEPGZHAS7QYA/graph.json","fetch_events":"https://pith.science/api/pith-number/W2BTC4SVRSFQECKEPGZHAS7QYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA/action/storage_attestation","attest_author":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA/action/author_attestation","sign_citation":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA/action/citation_signature","submit_replication":"https://pith.science/pith/W2BTC4SVRSFQECKEPGZHAS7QYA/action/replication_record"}},"created_at":"2026-05-18T00:03:49.150941+00:00","updated_at":"2026-05-18T00:03:49.150941+00:00"}