{
  "id": "1810.08199",
  "version": "v1",
  "published": "2018-10-18T09:24:24.000Z",
  "updated": "2018-10-18T09:24:24.000Z",
  "title": "Universal $d=1$ flatband generator from compact localized states",
  "authors": [
    "Wulayimu Maimaiti",
    "Sergej Flach",
    "Alexei Andreanov"
  ],
  "comment": "16 pages, 5 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "The band structure of some translationally invariant lattice Hamiltonians contains strictly dispersionless flatbands(FB). These are induced by destructive interference, and typically host compact localized eigenstates (CLS) which occupy a finite number $U$ of unit cells. FBs are important due to macroscopic degeneracy and consequently due to their high sensitivity and strong response to different types of weak perturbations. We use a recently introduced classification of FB networks based on CLS properties, and extend the FB Hamiltonian generator introduced in Phys. Rev. B 95, 115135 (2017) to an arbitrary number $\\nu$ of bands in the band structure, and arbitrary size $U$ of a CLS. The FB Hamiltonian is a solution to equations that we identify with an inverse eigenvalue problem. These can be solved only numerically in general. By imposing additional constraints, e.g. a chiral symmetry, we are able to find analytical solutions to the inverse eigenvalue problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-18T09:24:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact localized states",
      "invariant lattice hamiltonians contains",
      "flatband generator",
      "host compact localized eigenstates",
      "contains strictly dispersionless flatbands"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}