{
  "id": "1812.02701",
  "version": "v1",
  "published": "2018-12-06T18:34:51.000Z",
  "updated": "2018-12-06T18:34:51.000Z",
  "title": "Kinetic theory of spin superdiffusion in Heisenberg spin chains at high temperature",
  "authors": [
    "Sarang Gopalakrishnan",
    "Romain Vasseur"
  ],
  "comment": "6 pages, 1 figure",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "cond-mat.str-el",
    "quant-ph"
  ],
  "abstract": "We address the nature of spin transport in the integrable XXZ spin chain, focusing on the isotropic Heisenberg limit. We calculate the diffusion constant using a kinetic picture based on generalized hydrodynamics: we find that it diverges, and show that a self-consistent treatment of this divergence gives superdiffusion, with an effective time-dependent diffusion constant that scales as $D(t) \\sim t^{1/3} \\log^{2/3} t$. This exponent had previously been observed in large-scale numerical simulations, but had not been theoretically explained. Our results also make clear why the anomalous diffusion in the present case is a qualitatively different phenomenon from Levy flights and other phenomena in random systems. We briefly discuss XXZ models with easy-axis anisotropy $\\Delta > 1$; for these our treatment predicts diffusion, with a diffusion constant $D$ that saturates at large anisotropy, and diverges as the Heisenberg limit is approached, as $D \\sim (\\Delta - 1)^{-1/2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-06T18:34:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg spin chains",
      "high temperature",
      "spin superdiffusion",
      "kinetic theory",
      "treatment predicts diffusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}