{
  "id": "1810.12931",
  "version": "v1",
  "published": "2018-10-30T18:01:21.000Z",
  "updated": "2018-10-30T18:01:21.000Z",
  "title": "Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems",
  "authors": [
    "Jagannath Sutradhar",
    "Subroto Mukerjee",
    "Rahul Pandit",
    "Sumilan Banerjee"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Mo- tivated by this, we study transport in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its generalizations to 2d and 3d. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with localized states, to a metal, with extended states having (a) ballistic transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport (3d); precisely at the transition, the system displays sub-diffusive critical states. We calculate the beta function $\\beta(g) = dln(g)/dln(L)$ and show that, in 1d and 2d, single-parameter scaling is unable to describe the transition. Further- more, the conductances show strong non-monotonic variations with L and an intricate structure of resonant peaks and subpeaks. In 1d the positions of these peaks can be related precisely to the prop- erties of the number that characterizes the quasiperiodicity of the potential; and the L-dependence of the Thouless conductance is multifractal. We find that, as d increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our results for $\\beta(g)$ are reasonably well approximated by single-parameter scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-30T18:01:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82D30"
    ],
    "keywords": [
      "single-parameter scaling",
      "quasiperiodic systems",
      "localization transition",
      "multifractality",
      "thouless conductance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}