{
  "id": "1906.10167",
  "version": "v1",
  "published": "2019-06-24T18:50:32.000Z",
  "updated": "2019-06-24T18:50:32.000Z",
  "title": "Slow propagation in some disordered quantum spin chains",
  "authors": [
    "Bruno Nachtergaele",
    "Jake Reschke"
  ],
  "categories": [
    "math-ph",
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "We introduce the notion of transmission time to study the dynamics of disordered quantum spin chains and prove results relating its behavior to many-body localization properties. We also study two versions of the so-called Local Integrals of Motion (LIOM) representation of spin chain Hamiltonians and their relation to dynamical many-body localization. We prove that uniform-in-time dynamical localization expressed by a zero-velocity Lieb-Robinson bound implies the existence of a LIOM representation of the dynamics as well as a weak converse of this statement. We also prove that for a class of spin chains satisfying a form of exponential dynamical localization, sparse perturbations result in a dynamics in which transmission times diverge at least as a power law of distance, with a power for which we provide lower bound that diverges with increasing sparseness of the perturbation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-24T18:50:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C10",
      "82C44"
    ],
    "keywords": [
      "disordered quantum spin chains",
      "slow propagation",
      "zero-velocity lieb-robinson bound implies",
      "spin chain hamiltonians",
      "sparse perturbations result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}