{"paper":{"title":"Lattice fermion simulation of spontaneous time-reversal symmetry breaking in a helical Luttinger liquid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Helical liquid enters gapped phase with broken time-reversal symmetry","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"C. W. J. Beenakker, J. S\\'anchez Fern\\'an, V. A. Zakharov","submitted_at":"2026-01-14T15:32:20Z","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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Helical liquid enters gapped phase with broken time-reversal symmetry","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cf8e41b6131c94c8293d98f555a764e2c2479b65a2f5400f838f14ac68829fec"},"source":{"id":"2601.09563","kind":"arxiv","version":2},"verdict":{"id":"157dd350-8039-4dfa-93a6-e32b34c5c48d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T14:41:56.624119Z","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.","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","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.","pith_extraction_headline":"Helical liquid enters gapped phase with broken time-reversal symmetry"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.09563/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":35,"sample":[{"doi":"","year":null,"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","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"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","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"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","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"M. Z. Hasan and C. L. Kane,Topological insulators, Rev. Mod. Phys.82, 3045 (2010)","work_id":"d6f66d97-61e8-4ce3-b7c9-4daa3ab0b1a2","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"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","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"02d1b80022e2386f542e26c7dc71eb8495ed855b05435f7e5be9ad2a1a202111","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"fee2408e87814126e45c1b6f2dcad8d74dc06d46ab921a97720f3c6fdc030336"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}