{
  "id": "2310.14074",
  "version": "v1",
  "published": "2023-10-21T17:41:01.000Z",
  "updated": "2023-10-21T17:41:01.000Z",
  "title": "Localization renormalization and quantum Hall systems",
  "authors": [
    "Bartholomew Andrews",
    "Dominic Reiss",
    "Fenner Harper",
    "Rahul Roy"
  ],
  "comment": "10+9 pages, 7+4 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "The obstruction to constructing localized degrees of freedom is a signature of several interesting condensed matter phases. We introduce a localization renormalization procedure that harnesses this property, and apply our method to distinguish between topological and trivial phases in quantum Hall and Chern insulators. By iteratively removing a fraction of maximally-localized orthogonal basis states, we find that the localization length in the residual Hilbert space exhibits a power-law divergence as the fraction of remaining states approaches zero, with an exponent of $\\nu=0.5$. In sharp contrast, the localization length converges to a system-size-independent constant in the trivial phase. We verify this scaling using a variety of algorithms to truncate the Hilbert space, and show that it corresponds to a statistically self-similar expansion of the real-space projector. This result accords with a renormalization group picture and motivates the use of localization renormalization as a versatile numerical diagnostic for quantum Hall insulators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-21T17:41:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hall systems",
      "trivial phase",
      "renormalization group picture",
      "localization length converges",
      "quantum hall insulators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}