{
  "id": "2408.02016",
  "version": "v1",
  "published": "2024-08-04T12:53:55.000Z",
  "updated": "2024-08-04T12:53:55.000Z",
  "title": "Dynamics of many-body localized systems: logarithmic lightcones and $\\log \\, t$-law of $α$-Rényi entropies",
  "authors": [
    "Daniele Toniolo",
    "Sougato Bose"
  ],
  "comment": "12 pages plus references",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In the context of the Many-Body-Localization phenomenology we consider arbitrarily large one-dimensional spin systems. The XXZ model with disorder is a prototypical example. Without assuming the existence of exponentially localized integrals of motion (LIOMs), but assuming instead a logarithmic lightcone we rigorously evaluate the dynamical generation of $ \\alpha$-R\\'enyi entropies, $ 0< \\alpha<1 $ close to one, obtaining a $\\log \\, t$-law. Assuming the existence of LIOMs we prove that the Lieb-Robinson (L-R) bound of the system's dynamics has a logarithmic lightcone and show that the dynamical generation of the von Neumann entropy, from a generic initial product state, has for large times a $ \\log \\, t$-shape. L-R bounds, that quantify the dynamical spreading of local operators, may be easier to measure in experiments in comparison to global quantities such as entanglement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-04T12:53:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "logarithmic lightcone",
      "many-body localized systems",
      "rényi entropies",
      "arbitrarily large one-dimensional spin systems",
      "generic initial product state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}