{
  "id": "2406.01984",
  "version": "v1",
  "published": "2024-06-04T05:51:52.000Z",
  "updated": "2024-06-04T05:51:52.000Z",
  "title": "Unified one-parameter scaling function for Anderson localization transitions in non-reciprocal non-Hermitian systems",
  "authors": [
    "C. Wang",
    "Wenxue He",
    "X. R. Wang",
    "Hechen Ren"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling function using the participation ratio as the scaling variable. Employing a highly accurate numerical procedure based on exact diagonalization, we demonstrate that this one-parameter scaling function can describe Anderson localization transitions of non-reciprocal non-Hermitian systems in one and two dimensions of symmetry classes AI and A. The critical exponents of correlation lengths depend on symmetries and dimensionality only, a typical feature of universality. Moreover, we derive a complex-gap equation based on the self-consistent Born approximation that can determine the disorder at which the point gap closes. The obtained disorders match perfectly the critical disorders of Anderson localization transitions from the one-parameter scaling function. Finally, we show that the one-parameter scaling function is also valid for Anderson localization transitions in reciprocal non-Hermitian systems such as two-dimensional class AII$^\\dagger$ and can, thus, serve as a unified scaling function for disordered non-Hermitian systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-04T05:51:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anderson localization transitions",
      "non-reciprocal non-hermitian systems",
      "unified one-parameter scaling function",
      "two-dimensional class aii",
      "conventional one-parameter scaling theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}