{
  "id": "2405.15220",
  "version": "v1",
  "published": "2024-05-24T05:19:40.000Z",
  "updated": "2024-05-24T05:19:40.000Z",
  "title": "Hybrid scaling theory of localization transition in a non-Hermitian disorder Aubry-André model",
  "authors": [
    "Yue-Mei Sun",
    "Xin-Yu Wang",
    "Zi-Kang Wang",
    "Liang-Jun Zhai"
  ],
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "In this paper, we study the critical behaviors in the non-Hermtian disorder Aubry-Andr\\'{e} (DAA) model, and we assume the non-Hermiticity is introduced by the nonreciprocal hopping. We employ the localization length $\\xi$, the inverse participation ratio ($\\rm IPR$), and the real part of the energy gap between the first excited state and the ground state $\\Delta E$ as the character quantities to describe the critical properties of the localization transition. By preforming the scaling analysis, the critical exponents of the non-Hermitian Anderson model and the non-Hermitian DAA model are obtained, and these critical exponents are different from their Hermitian counterparts, indicating the Hermitian and non-Hermitian disorder and DAA models belong to different universe classes. The critical exponents of non-Hermitian DAA model are remarkably different from both the pure non-Hermitian AA model and the non-Hermitian Anderson model, showing that disorder is a independent relevant direction at the non-Hermitian AA model. We further propose a hybrid scaling theory to describe the critical behavior in the overlapping critical region constituted by the critical regions of non-Hermitian DAA model and the non-Hermitian Anderson localization transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-24T05:19:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hybrid scaling theory",
      "non-hermitian disorder",
      "non-hermitian daa model",
      "non-hermitian anderson model",
      "critical exponents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}