{
  "id": "2501.13190",
  "version": "v1",
  "published": "2025-01-22T19:45:12.000Z",
  "updated": "2025-01-22T19:45:12.000Z",
  "title": "Duality breaking, mobility edges, and the connection between topological Aubrey-André and quantum Hall insulators in atomic wires with fermions",
  "authors": [
    "Bar Alluf",
    "C. A. R. Sa de Melo"
  ],
  "comment": "16 pages, 14 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.dis-nn"
  ],
  "abstract": "It is well known that the Aubry-Andr{\\'e} model lacks mobility edges due to its energy-independent self-duality but may exhibit edge states. When duality is broken, we show that mobility regions arise and non-trivial topological phases emerge. By varying the degree of duality breaking, we identify mobility regions and establish a connection between Aubry-Andr{\\'e} atomic wires with fermions and quantum Hall systems for a family of Hamiltonians that depends on the relative phase of laser fields, viewed as a synthetic dimension. Depending on the filling factor and the degree of duality breaking, we find three classes of non-trivial phases: conventional topological insulator, conventional topological Aubry-Andr{\\'e} insulator, and unconventional (hybrid) topological Aubry-Andr{\\'e} insulator. Finally, we discuss appropriate Chern numbers that illustrate the classification of topological phases of localized fermions in atomic wires.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-22T19:45:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hall insulators",
      "atomic wires",
      "duality breaking",
      "topological",
      "connection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}