{
  "id": "2203.07415",
  "version": "v1",
  "published": "2022-03-14T18:19:48.000Z",
  "updated": "2022-03-14T18:19:48.000Z",
  "title": "Scaling of Fock-space propagator and multifractality across the many-body localization transition",
  "authors": [
    "Jagannath Sutradhar",
    "Soumi Ghosh",
    "Sthitadhi Roy",
    "David E. Logan",
    "Subroto Mukerjee",
    "Sumilan Banerjee"
  ],
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "We implement a recursive Green function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random onsite potential. We show that the typical value of the imaginary part of the local FS self-energy, \\Delta_t, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition; and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension D_s extracted from \\Delta_t jumps discontinuously across the transition, from D_s<1 in the MBL phase to D_s= 1 in the thermal phase. Moreover, \\Delta_t follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a non-ergodic volume in the thermal phase diverges with a Kosterlitz-Thouless like essential singularity at the critical point W_c, and controls the continuous vanishing of \\Delta_t as W_c is approached. In contrast, a correlation length ({\\xi}) extracted from \\Delta_t exhibits a power-law divergence on approaching W_c from the MBL phase.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-14T18:19:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body localization transition",
      "fock-space propagator",
      "multifractality",
      "random onsite potential",
      "thermal phase diverges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}