{
  "id": "2403.01974",
  "version": "v2",
  "published": "2024-03-04T12:16:35.000Z",
  "updated": "2024-08-16T09:28:52.000Z",
  "title": "Renormalization group for Anderson localization on high-dimensional lattices",
  "authors": [
    "Boris L. Altshuler",
    "Vladimir E. Kravtsov",
    "Antonello Scardicchio",
    "Piotr Sierant",
    "Carlo Vanoni"
  ],
  "comment": "13 pages, 12 figures. Comments are welcome!",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "We discuss the dependence of the critical properties of the Anderson model on the dimension $d$ in the language of $\\beta$-function and renormalization group recently introduced in Ref.[arXiv:2306.14965] in the context of Anderson transition on random regular graphs. We show how in the delocalized region, including the transition point, the one-parameter scaling part of the $\\beta$-function for the fractal dimension $D_{1}$ evolves smoothly from its $d=2$ form, in which $\\beta_2\\leq 0$, to its $\\beta_\\infty\\geq 0$ form, which is represented by the regular random graph (RRG) result. We show how the $\\epsilon=d-2$ expansion and the $1/d$ expansion around the RRG result can be reconciled and how the initial part of a renormalization group trajectory governed by the irrelevant exponent $y$ depends on dimensionality. We also show how the irrelevant exponent emerges out of the high-gradient terms of expansion in the nonlinear sigma-model and put forward a conjecture about a lower bound for the fractal dimension. The framework introduced here may serve as a basis for investigations of disordered many-body systems and of more general non-equilibrium quantum systems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-08-16T09:28:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anderson localization",
      "high-dimensional lattices",
      "general non-equilibrium quantum systems",
      "fractal dimension",
      "random regular graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}