{
  "id": "1808.02054",
  "version": "v1",
  "published": "2018-08-06T18:14:55.000Z",
  "updated": "2018-08-06T18:14:55.000Z",
  "title": "Temperature dependence of butterfly effect in a classical many-body system",
  "authors": [
    "Thomas Bilitewski",
    "Subhro Bhattacharjee",
    "Roderich Moessner"
  ],
  "comment": "6+4 pages, 4+8 figures, ancillary files include videos of the dynamics",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterise many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered correlator. Due to the emergence of a spin liquid phase, the chaotic dynamics extends all the way to zero temperature. We thus determine the full temperature dependence of two complementary aspects of the butterfly effect: the Lyapunov exponent, $\\mu$, and the butterfly speed, $v_b$, and study their interrelations with usual measures of spin dynamics such as the spin-diffusion constant, $D$ and spin-autocorrelation time, $\\tau$. We find that they all exhibit power law behaviour at low temperature, consistent with scaling of the form $D\\sim v_b^2/\\mu$ and $\\tau^{-1}\\sim T$. The vanishing of $\\mu\\sim T^{0.48}$ is parametrically slower than that of the corresponding quantum bound, $\\mu\\sim T$, raising interesting questions regarding the semi-classical limit of such spin systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-06T18:14:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical many-body system",
      "butterfly effect",
      "characterise many-body chaos",
      "spin liquid phase",
      "chaotic dynamics extends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}