{
  "id": "2005.10814",
  "version": "v1",
  "published": "2020-05-21T17:49:52.000Z",
  "updated": "2020-05-21T17:49:52.000Z",
  "title": "Information scrambling at finite temperature in local quantum systems",
  "authors": [
    "Subhayan Sahu",
    "Brian Swingle"
  ],
  "comment": "28+17 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "hep-th",
    "quant-ph"
  ],
  "abstract": "This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, $m$, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature $T$. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O($N$) non-linear sigma model, which is analytically tractable at large $N$. Using the ladder diagram technique, we find that operators spread at a speed $\\sqrt{T/m}$ at low temperatures, $T\\ll m$. In contrast to the numerical findings of spin chain, the large $N$ computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-21T17:49:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local quantum systems",
      "finite temperature",
      "information scrambling",
      "large scale tensor network numerics",
      "report large scale tensor network"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}