{
  "id": "2209.14253",
  "version": "v1",
  "published": "2022-09-28T17:18:00.000Z",
  "updated": "2022-09-28T17:18:00.000Z",
  "title": "Universality in the tripartite information after global quenches",
  "authors": [
    "Vanja Marić",
    "Maurizio Fagotti"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "quant-ph"
  ],
  "abstract": "We consider macroscopically large 3-partitions $(A,B,C)$ of connected subsystems $A\\cup B \\cup C$ in infinite spin chains and study the R\\'enyi-$\\alpha$ tripartite information $I_3^{(\\alpha)}(A,B,C)$. At equilibrium in clean 1D systems with local Hamiltonians it generally vanishes. A notable exception is the ground state of conformal critical systems, in which $I_3^{(\\alpha)}(A,B,C)$ is known to be a universal function of the cross ratio $x=|A||C|/[(|A|+|B|)(|C|+|B|)]$, where $|A|$ denotes $A$'s length. We identify three classes of states for which time evolution under translationally invariant Hamiltonians can build up (R\\'enyi) tripartite information with a universal dependency on $x$. We report a numerical study of $I_3^{(\\alpha)}$ in systems that are dual to free fermions, propose a field-theory description, and conjecture their asymptotic behaviour for $\\alpha=2$ in general and for generic $\\alpha$ in a subclass of systems. This allows us to infer the value of $I_3^{(\\alpha)}$ in the scaling limit $x\\rightarrow 1^-$, which we call \"residual tripartite information\". If nonzero, our analysis points to a universal residual value $-\\log 2$ independently of the R\\'enyi index $\\alpha$, and hence applies also to the genuine (von Neumann) tripartite information.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-28T17:18:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global quenches",
      "universality",
      "residual tripartite information",
      "clean 1d systems",
      "infinite spin chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}