{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:XVXI34KCSB3JDUO2OVZJADGQAT","short_pith_number":"pith:XVXI34KC","schema_version":"1.0","canonical_sha256":"bd6e8df142907691d1da7572900cd004cba3165fd4b05f194940aef0e78a40b3","source":{"kind":"arxiv","id":"0912.3272","version":2},"attestation_state":"computed","paper":{"title":"Topological Order and Quantum Criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Claudio Castelnovo, Matthias Troyer, Simon Trebst","submitted_at":"2009-12-16T21:45:08Z","abstract_excerpt":"In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely certain deformations of the toric code model, that exhibit continuous quantum phase transitions. One such deformation leads to a Lorentz-invariant transition in the 3D Ising universality class. An alternative deformation gives rise to a so-called conformal quantum critical point where equal-time correlations become conformally invariant and can be related to th"},"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":"0912.3272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2009-12-16T21:45:08Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"681871d9b714222012c50602009be97b95803b76299ffc21d8262f7803a9ca0b","abstract_canon_sha256":"e05601bb75110577bcacbf0c1af3e64852e4fb467f5636c7dfa0a4511b262e18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:16.253404Z","signature_b64":"RNnI/8ILImZBbPk2qaDdOEWRyKdUl3MwsvnmbumjWutwP8xKdaZOpGbtoFzIVydDZsw/sJz/dqEFz6L5AM3EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd6e8df142907691d1da7572900cd004cba3165fd4b05f194940aef0e78a40b3","last_reissued_at":"2026-05-18T02:10:16.252751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:16.252751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Order and Quantum Criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.str-el","authors_text":"Claudio Castelnovo, Matthias Troyer, Simon Trebst","submitted_at":"2009-12-16T21:45:08Z","abstract_excerpt":"In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely certain deformations of the toric code model, that exhibit continuous quantum phase transitions. One such deformation leads to a Lorentz-invariant transition in the 3D Ising universality class. An alternative deformation gives rise to a so-called conformal quantum critical point where equal-time correlations become conformally invariant and can be related to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3272","kind":"arxiv","version":2},"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":"0912.3272","created_at":"2026-05-18T02:10:16.252841+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.3272v2","created_at":"2026-05-18T02:10:16.252841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3272","created_at":"2026-05-18T02:10:16.252841+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVXI34KCSB3J","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVXI34KCSB3JDUO2","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVXI34KC","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.20619","citing_title":"Extracting conserved operators from a projected entangled pair state","ref_index":75,"is_internal_anchor":true},{"citing_arxiv_id":"2605.06069","citing_title":"Topological spin freezing in frustrated quantum materials","ref_index":116,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT","json":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT.json","graph_json":"https://pith.science/api/pith-number/XVXI34KCSB3JDUO2OVZJADGQAT/graph.json","events_json":"https://pith.science/api/pith-number/XVXI34KCSB3JDUO2OVZJADGQAT/events.json","paper":"https://pith.science/paper/XVXI34KC"},"agent_actions":{"view_html":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT","download_json":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT.json","view_paper":"https://pith.science/paper/XVXI34KC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.3272&json=true","fetch_graph":"https://pith.science/api/pith-number/XVXI34KCSB3JDUO2OVZJADGQAT/graph.json","fetch_events":"https://pith.science/api/pith-number/XVXI34KCSB3JDUO2OVZJADGQAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT/action/storage_attestation","attest_author":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT/action/author_attestation","sign_citation":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT/action/citation_signature","submit_replication":"https://pith.science/pith/XVXI34KCSB3JDUO2OVZJADGQAT/action/replication_record"}},"created_at":"2026-05-18T02:10:16.252841+00:00","updated_at":"2026-05-18T02:10:16.252841+00:00"}