{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KICJSKLGYN7QJGAPOJIWRMAEAV","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":"27ed1f1878551101319ecf6a698f2bfa4bda7a06062e468f8b355900faa2bf39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-03-10T08:55:48Z","title_canon_sha256":"340815fc44cb6ab6721ae288bc0c571f12d0a18798969e4861e3b0ce727f99e8"},"schema_version":"1.0","source":{"id":"1803.03779","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03779","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03779v2","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03779","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"KICJSKLGYN7Q","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KICJSKLGYN7QJGAP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KICJSKLG","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:52646867b7d29979cfe0ff29f0b68604d7725873d5056f46ce914578a3cae2ca","target":"graph","created_at":"2026-05-17T23:47:31Z","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 study the spin-$\\frac{1}{2}$ antiferromagnetic Heisenberg model on an infinity-by-$N$ square lattice for even $N$'s up to $14$. Previously, the nonlinear sigma model perturbatively predicts that its spin rotational symmetry asymptotically breaks when $N\\rightarrow \\infty$, i.e., when it is two-dimensional (2D). However, we identified a critical width $N_c = 10$ for which this symmetry breaks spontaneously. It defines a dimensional transition from one-dimension (1D) including quasi-1D to 2D. The finite-size effect differs from that of the $N$-by-$N$ lattice. The ground state (GS) energy per ","authors_text":"Kwang S. Kim, Lihua Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-03-10T08:55:48Z","title":"Quantum Dimensional Transition in Spin-$\\frac{1}{2}$ Antiferromagnetic Heisenberg Model on A Square Lattice and Space Reduction in Matrix Product State"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03779","kind":"arxiv","version":2},"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":"sha256:664e44ec82ce84df491fbbaeb5d896ce5430e8f29aee16d78b2f9e11fc6d7299","target":"record","created_at":"2026-05-17T23:47:31Z","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":"27ed1f1878551101319ecf6a698f2bfa4bda7a06062e468f8b355900faa2bf39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2018-03-10T08:55:48Z","title_canon_sha256":"340815fc44cb6ab6721ae288bc0c571f12d0a18798969e4861e3b0ce727f99e8"},"schema_version":"1.0","source":{"id":"1803.03779","kind":"arxiv","version":2}},"canonical_sha256":"5204992966c37f04980f725168b004054a9151c27d7ba0a27bfb8dc9bb5fa6f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5204992966c37f04980f725168b004054a9151c27d7ba0a27bfb8dc9bb5fa6f4","first_computed_at":"2026-05-17T23:47:31.391297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.391297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fn2yZzvmasAZljIU0MC2IzcQr2KwppLN8JOc7rJw9BC2efv5bI0RDVBERv24UbCyjyDEmt9K9MRgAnFkOKPlAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.391747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03779","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:664e44ec82ce84df491fbbaeb5d896ce5430e8f29aee16d78b2f9e11fc6d7299","sha256:52646867b7d29979cfe0ff29f0b68604d7725873d5056f46ce914578a3cae2ca"],"state_sha256":"8333069bcd64b46a13f18e153668ab1da543e7752ab6d2dc1e148ee17360e9fb"}