{"paper":{"title":"One-dimensional non-Hermitian band structures as Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","math.MP"],"primary_cat":"math-ph","authors_text":"Heming Wang, Lingling Fan, Shanhui Fan","submitted_at":"2024-01-22T02:33:53Z","abstract_excerpt":"We present the viewpoint of treating one-dimensional band structures as Riemann surfaces, linking the unique properties of non-Hermiticity to the geometry and topology of the Riemann surface. Branch cuts and branch points play a significant role when this viewpoint is applied to both the open-boundary spectrum and the braiding structure. An open-boundary spectrum is interpreted as branch cuts connecting certain branch points, and its consistency with the monodromy representation severely limits its possible morphology. A braid word for the Brillouin zone can be read off from its intersections "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11661","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.11661/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}