{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2DVVO32V6VLF35OV2LRASHXLK6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1491da273183f67cd05aec2afd05531587f85707077f3203b8db259258c1abed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-06-30T19:53:49Z","title_canon_sha256":"92d369946b906172f97effd6461a54c2fcee546fd8423b22d218039ca6154875"},"schema_version":"1.0","source":{"id":"1606.09639","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09639","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09639v5","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09639","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"2DVVO32V6VLF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2DVVO32V6VLF35OV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2DVVO32V","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:a7a8b3a95c9b39a6cc1f657f7e2e984dc70e87fe5673f3ba186f7dffed97264e","target":"graph","created_at":"2026-05-18T00:42:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\\mathbb{Z}_2$-topological order (or toric code","authors_text":"Huan He, Jia-Wei Mei, Ji-Yao Chen, Xiao-Gang Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-06-30T19:53:49Z","title":"Gapped spin liquid with $\\mathbb{Z}_2$-topological order for kagome Heisenberg model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09639","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b1d3758a77c8ea2604c8a609c3095eb2cef6429802bea652a69c5555cf9654e6","target":"record","created_at":"2026-05-18T00:42:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1491da273183f67cd05aec2afd05531587f85707077f3203b8db259258c1abed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2016-06-30T19:53:49Z","title_canon_sha256":"92d369946b906172f97effd6461a54c2fcee546fd8423b22d218039ca6154875"},"schema_version":"1.0","source":{"id":"1606.09639","kind":"arxiv","version":5}},"canonical_sha256":"d0eb576f55f5565df5d5d2e2091eeb5788ff7c237283930ad3c843ffd80efd65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0eb576f55f5565df5d5d2e2091eeb5788ff7c237283930ad3c843ffd80efd65","first_computed_at":"2026-05-18T00:42:18.949732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:18.949732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wkgg0rrY0Nwm8NC8BxTYHTS+/2ViaQ5Pa3TiBWkdYayNLWLCdr5mvNaCuz7rDrG6f0MD/kSLXfTf46eucXo8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:18.950412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09639","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1d3758a77c8ea2604c8a609c3095eb2cef6429802bea652a69c5555cf9654e6","sha256:a7a8b3a95c9b39a6cc1f657f7e2e984dc70e87fe5673f3ba186f7dffed97264e"],"state_sha256":"35204c52b1fb0cf5230c900f6ac84387c5b0a4e5c434156256a86a3c7e38b2c7"}