{
  "id": "2402.10123",
  "version": "v2",
  "published": "2024-02-15T17:21:35.000Z",
  "updated": "2024-06-11T13:44:43.000Z",
  "title": "Role of Fock-space correlations in many-body localization",
  "authors": [
    "Thibault Scoquart",
    "Igor V. Gornyi",
    "Alexander D. Mirlin"
  ],
  "comment": "29 pages, 15 figures",
  "journal": "Phys. Rev. B 109, 214203 - Published 7 June 2024",
  "doi": "10.1103/PhysRevB.109.214203",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "Models of many-body localization (MBL) can be represented as tight-binding models in the many-body Hilbert space (Fock space). We explore the role of correlations between matrix elements of the effective Fock-space Hamiltonians in the scaling of MBL critical disorder $W_c(n)$ with the size $n$ of the system. For this purpose, we consider five models, which all have the same distributions of diagonal (energy) and off-diagonal (\"hopping\") Fock-space matrix elements but different Fock-space correlations. These include quantum-dot (QD) and one-dimensional (1D) MBL models, their modifications (uQD and u1D models) with removed correlations of off-diagonal matrix elements, as well a quantum random energy model (QREM) with no correlations at all. Our numerical results are in full consistency with analytical arguments predicting $n^{3/4} (\\ln n)^{-1/4} \\lesssim W_c \\lesssim n \\ln n$ for the scaling of $W_c(n)$ in the QD model (we find $W_c \\sim n$ numerically), $W_c(n) \\sim \\text{const.}$ for the 1D model, $W_c \\sim n \\ln n$ for the uQD and u1D models without off-diagonal correlations, and $W_c \\sim n^{1/2} \\ln n$ for QREM. The key difference between the QD and 1D models is in the structure of correlations of many-body energies. Removing off-diagonal Fock-space correlations makes both these models \"maximally chaotic\". Our findings demonstrate that the scaling of $W_c(n)$ for MBL transitions is governed by a combined effect of Fock-space correlations of diagonal and off-diagonal matrix elements.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-11T13:44:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body localization",
      "off-diagonal matrix elements",
      "u1d models",
      "quantum random energy model",
      "fock-space matrix elements"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}