{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E24JLCMXXSBRYHQQ5MUB5UDWQ7","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":"5b4b2496520a29df5e0d80b0e589a7ceac0309c17b89330f77b806717c57b542","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-01-14T15:32:20Z","title_canon_sha256":"f9ebc4842baf5bb3c5fdbee3cd03896df5e018c6e3e70901658be80ae793c350"},"schema_version":"1.0","source":{"id":"2601.09563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.09563","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2601.09563v2","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.09563","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"E24JLCMXXSBR","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"E24JLCMXXSBRYHQQ","created_at":"2026-05-22T01:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"E24JLCMX","created_at":"2026-05-22T01:03:16Z"}],"graph_snapshots":[{"event_id":"sha256:2457efee04edf7695827bec72034dd14323329b4a3cb541542ccbfec7d0a3b0c","target":"graph","created_at":"2026-05-22T01:03:16Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"A gapped phase with spontaneously broken time-reversal symmetry emerges when the Fermi level is tuned to the Dirac point and the Luttinger parameter crosses a critical value."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The tangent dispersion relation faithfully captures the low-energy physics of the helical Luttinger liquid without introducing spurious artifacts, and the finite-lattice tensor network results extrapolate to the infinite-system analytic limit."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Numerical lattice simulation confirms spontaneous time-reversal symmetry breaking and gap opening in a helical Luttinger liquid at the Dirac point above a critical Luttinger parameter."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Helical liquid enters gapped phase with broken time-reversal symmetry"}],"snapshot_sha256":"cf8e41b6131c94c8293d98f555a764e2c2479b65a2f5400f838f14ac68829fec"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"fee2408e87814126e45c1b6f2dcad8d74dc06d46ab921a97720f3c6fdc030336"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.09563/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend a recently developed \"tangent fermion\" method to discretize the Hamiltonian of a helical Luttinger liquid on a one-dimensional lattice, including two-particle backscattering processes that may open a gap in the spectrum. The fermion-doubling obstruction of the sine dispersion is avoided by working with a tangent dispersion, preserving the time-reversal symmetry of the Hamiltonian. The numerical results from a tensor network calculation on a finite lattice confirm the expectation from infinite-system analytics, that a gapped phase with spontaneously broken time-reversal symmetry emerg","authors_text":"C. W. J. Beenakker, J. S\\'anchez Fern\\'an, V. A. Zakharov","cross_cats":["quant-ph"],"headline":"Helical liquid enters gapped phase with broken time-reversal symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-01-14T15:32:20Z","title":"Lattice fermion simulation of spontaneous time-reversal symmetry breaking in a helical Luttinger liquid"},"references":{"count":35,"internal_anchors":0,"resolved_work":35,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Intra-band scattering Point splitting [31, 32] is the operation that replaces the product of fermion fields at the same position by an infinitesimal displacement±ϵ, ψσ(x)ψσ(x)7→ 1 2 ψσ(x)ψσ(x+ϵ)+ 1 2 ","work_id":"745f6806-4c82-4a14-b197-19800223a27a","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"The termK n is again a second derivative, X n Kn = 2 X k (1−cos 2ka)c † k↑ck↓,(A10) which becomes irrelevant in the long-wave length regime","work_id":"44c413c2-3c59-466c-9aec-de0017dbed6c","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"For that purpose we make the replacementsc nσ ↔ cn+1,σ, with an error that vanishes askain the long-wave length limit","work_id":"2d3fa5f4-132f-4a13-b37c-8a2dff9760f7","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"M. Z. Hasan and C. L. Kane,Topological insulators, Rev. Mod. Phys.82, 3045 (2010)","work_id":"d6f66d97-61e8-4ce3-b7c9-4daa3ab0b1a2","year":2010},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"J. Maciejko, T. L. Hughes, and S.-C. Zhang,The quan- tum spin Hall effect, Annu. Rev. Condens. Matter Phys. 2, 31 (2011)","work_id":"a97e15ff-1481-4be9-8565-70449a67f6d0","year":2011}],"snapshot_sha256":"02d1b80022e2386f542e26c7dc71eb8495ed855b05435f7e5be9ad2a1a202111"},"source":{"id":"2601.09563","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-16T14:41:56.624119Z","id":"157dd350-8039-4dfa-93a6-e32b34c5c48d","model_set":{"reader":"grok-4.3"},"one_line_summary":"Numerical lattice simulation confirms spontaneous time-reversal symmetry breaking and gap opening in a helical Luttinger liquid at the Dirac point above a critical Luttinger parameter.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Helical liquid enters gapped phase with broken time-reversal symmetry","strongest_claim":"A gapped phase with spontaneously broken time-reversal symmetry emerges when the Fermi level is tuned to the Dirac point and the Luttinger parameter crosses a critical value.","weakest_assumption":"The tangent dispersion relation faithfully captures the low-energy physics of the helical Luttinger liquid without introducing spurious artifacts, and the finite-lattice tensor network results extrapolate to the infinite-system analytic limit."}},"verdict_id":"157dd350-8039-4dfa-93a6-e32b34c5c48d"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c16dea04f3634de96b205e7f9bc2ad35ee18c95ba4c59d9b3087a2171fac384b","target":"record","created_at":"2026-05-22T01:03:16Z","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":"5b4b2496520a29df5e0d80b0e589a7ceac0309c17b89330f77b806717c57b542","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2026-01-14T15:32:20Z","title_canon_sha256":"f9ebc4842baf5bb3c5fdbee3cd03896df5e018c6e3e70901658be80ae793c350"},"schema_version":"1.0","source":{"id":"2601.09563","kind":"arxiv","version":2}},"canonical_sha256":"26b8958997bc831c1e10eb281ed07687e2c2ee0edb11c91dc5134776f72cfa67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26b8958997bc831c1e10eb281ed07687e2c2ee0edb11c91dc5134776f72cfa67","first_computed_at":"2026-05-22T01:03:16.951886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:16.951886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9dd+kQufQ0QaOA9iIoWAOD3PzL7Bs3k1J6Nm1Dl9tmFVYr7Pep3k2dXxDchbpAq6BRF5mDrjk1lzotQcal7gAg==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:16.952868Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.09563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c16dea04f3634de96b205e7f9bc2ad35ee18c95ba4c59d9b3087a2171fac384b","sha256:2457efee04edf7695827bec72034dd14323329b4a3cb541542ccbfec7d0a3b0c"],"state_sha256":"dbe64553d0a3263916d0f48bd79905d2c0d0e8197dbf8d34288d80875309c64e"}