{
  "abstract": "We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25000",
  "author_total": 2,
  "authors": [
    {
      "name": "Simon Becker"
    },
    {
      "name": "Mengxuan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9kwq7z5qhm25q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25000",
  "fulltext_url": null,
  "id": "9kwq7z5qhm25q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25000",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214044359",
  "pdf_url": "https://arxiv.org/pdf/2609.25000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9kwq7z5qhm25q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:20Z",
      "native_id": "2609.25000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25000"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap",
  "title_text": "Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9kwq7z5qhm25q",
  "venue": "arXiv",
  "versions": []
}