{
  "abstract": "Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially fast in space. In two and three spatial dimensions, it is well understood for periodic insulators that exponentially-localized Wannier functions exist if and only if there exists an orthonormal basis for the Fermi projection with finite second moment (that is all basis elements satisfy $$\\int \\vert \\varvec{x}\\vert ^2 \\vert w(\\varvec{x})\\vert ^2 \\,\\text {d}{\\varvec{x}} < \\infty $$ ∫ | x | 2 | w ( x ) | 2 d x < ∞ ). In this work, we establish a similar result for non-periodic insulators in two spatial dimensions. In particular, we prove that if there exists an orthonormal basis for the Fermi projection which satisfies $$\\int \\vert \\varvec{x}\\vert ^{5 + \\varepsilon } \\vert w(\\varvec{x})\\vert ^2 \\,\\text {d}{\\varvec{x}} < \\infty $$ ∫ | x | 5 + ε | w ( x ) | 2 d x < ∞ for some $$\\varepsilon > 0$$ ε > 0 , then there also exists an orthonormal basis for the Fermi projection which decays exponentially fast in space. This result lends support to the Localization Dichotomy Conjecture for non-periodic systems recently proposed by Marcelli, Monaco, Moscolari, and Panati in [1, 2].",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham, NC, 27708, USA",
    "Department of Mathematics, University of California - Berkeley, 970 Evans Hall, Berkeley, CA, 94720-3840, USA",
    "Department of Mathematics, University of Minnesota - Twin Cities, 127 Vincent Hall, Minneapolis, MN, 55455, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jianfeng Lu",
      "orcid": "0000-0001-6255-5165"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Kevin D. Stubbs",
      "orcid": "0000-0003-0062-5097"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14fm3ja279jtj.bib",
  "cited_by": 5,
  "doi": "10.1007/s00205-026-02242-z",
  "fulltext_url": null,
  "id": "14fm3ja279jtj",
  "issns": [
    "0003-9527",
    "1432-0673"
  ],
  "landing_url": "https://doi.org/10.1007/s00205-026-02242-z",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W3120847083",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00205-026-02242-z.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/14fm3ja279jtj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W3120847083",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00205-026-02242-z"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Algebraic Localization Implies Exponential Localization in Non-periodic Insulators",
  "title_text": "Algebraic Localization Implies Exponential Localization in Non-periodic Insulators",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/14fm3ja279jtj",
  "venue": "Archive for Rational Mechanics and Analysis",
  "versions": []
}