{
  "id": "2003.01138",
  "version": "v1",
  "published": "2020-03-02T19:00:19.000Z",
  "updated": "2020-03-02T19:00:19.000Z",
  "title": "Mean-field theory of entanglement transitions from random tree tensor networks",
  "authors": [
    "Javier Lopez-Piqueres",
    "Brayden Ware",
    "Romain Vasseur"
  ],
  "comment": "5 pages main text, 8 pages supp mat",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cond-mat.str-el",
    "quant-ph"
  ],
  "abstract": "Entanglement phase transitions in quantum chaotic systems subject to projective measurements or in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-02T19:00:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field theory",
      "entanglement transition",
      "statistical mechanics model",
      "random tree tensor network states",
      "phase transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}