{"paper":{"title":"Topology and edge modes surviving criticality in non-Hermitian Floquet systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems.","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Longwen Zhou","submitted_at":"2026-02-13T04:01:55Z","abstract_excerpt":"The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocate the study of symmetry-protected topological phases (SPTs) to gapless regions. In this letter, we reveal gapless SPTs (gSPTs) in systems tuned out-of-equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases an"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that sublattice symmetry in one-dimensional non-Hermitian Floquet models permits a well-defined generalized Brillouin zone to which Cauchy's argument principle can be applied without additional restrictions at criticality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Non-Hermitian Floquet systems host gapless symmetry-protected topological phases with unified winding numbers and robust edge modes surviving at criticality.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"76c7e56f2ae8995a4bcf386dafded729c26f7edc30b0894a6c13dd39560b3eda"},"source":{"id":"2602.12588","kind":"arxiv","version":2},"verdict":{"id":"9d00579e-85a5-4183-aac5-653a62ebbe75","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T22:51:09.147747Z","strongest_claim":"We introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points.","one_line_summary":"Non-Hermitian Floquet systems host gapless symmetry-protected topological phases with unified winding numbers and robust edge modes surviving at criticality.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that sublattice symmetry in one-dimensional non-Hermitian Floquet models permits a well-defined generalized Brillouin zone to which Cauchy's argument principle can be applied without additional restrictions at criticality.","pith_extraction_headline":"Winding numbers defined via Cauchy's principle on generalized Brillouin zones unify topology for both gapped and gapless phases in non-Hermitian Floquet systems."},"references":{"count":91,"sample":[{"doi":"","year":null,"title":"The roles of disorder and interactions in non-Hermitian Floquet gSPTs also deserve more thorough explorations","work_id":"3e82c26b-9449-47c1-8388-0c6135269358","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"T. Scaffidi, D. E. Parker, and R. Vasseur, Gapless Symmetry-Protected Topological Order, Phys. Rev. X7, 041048 (2017)","work_id":"b110b6f6-ccd6-4a39-971a-c5a77d009645","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"R. Verresen, R. Thorngren, N. G. Jones, and F. Pollmann, Gapless Topological Phases and Symmetry- Enriched Quantum Criticality, Phys. Rev. X11, 041059 (2021)","work_id":"9c111808-7cf7-4a28-9cd0-69185264f5e1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Y. Baum, T. Posske, I. C. Fulga, B. Trauzettel, and A. Stern, Coexisting Edge States and Gapless Bulk in Topo- logical States of Matter, Phys. Rev. Lett.114, 136801 (2015)","work_id":"7c70e4d3-6d80-4036-a8c4-0352fdfd41c7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"A. Keselman and E. Berg, Gapless symmetry-protected topological phase of fermions in one dimension, Phys. Rev. B91, 235309 (2015)","work_id":"b21d03b4-6655-4177-9d17-079a8f481784","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":91,"snapshot_sha256":"7dafc59feb633765288dabb07a1c6dd5c32c9e80face9977a7d5bbe4fe37add5","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5e1bf7f0ded843da3883f50aa18dcd84561c9a22605511a1e75f016ad13abb99"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}