{
  "id": "1906.10701",
  "version": "v1",
  "published": "2019-06-25T18:00:07.000Z",
  "updated": "2019-06-25T18:00:07.000Z",
  "title": "Statistics of correlations across the many-body localization transition",
  "authors": [
    "Luis Colmenarez",
    "Paul A. McClarty",
    "Masudul Haque",
    "David J. Luitz"
  ],
  "comment": "17 pages, 14 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of \\emph{eigenstate correlation functions} across the entire phase diagram. We find gaussian distributions at weak disorder, as predicted by pure ETH. At intermediate disorder -- in the thermal phase -- we find further evidence for \\emph{anomalous thermalization} in the form of heavy tails of the distributions. In the MBL phase, we observe peculiar features of the correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators skewed towards negative values; and a multimodal distribution for spin-flip correlators. A \\emph{quantitative quasi-degenerate perturbation theory} calculation of these correlators yields a surprising \\emph{agreement of the full distribution} with the exact results, revealing, in particular, the origin of the multiple peaks in the spin-flip correlator distribution as arising from the resonant and off-resonant admixture of spin configurations. The distribution of the $S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and Anderson insulator cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-25T18:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body localization transition",
      "ergodic quantum many-body systems satisfy",
      "correlation",
      "probability distribution",
      "correlator distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}