{
  "id": "2006.15465",
  "version": "v1",
  "published": "2020-06-27T23:22:24.000Z",
  "updated": "2020-06-27T23:22:24.000Z",
  "title": "Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking",
  "authors": [
    "Maxime Dupont",
    "Nicolas Laflorencie",
    "Gabriel Lemarié"
  ],
  "comment": "21 pages, 16 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number $K=2$. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a non-trivial algebraic vanishing BEC density together with a non-ergodic occupation in real-space. These peculiar properties can be analytically captured by a simple toy-model on the Cayley tree which provides a physical picture of the Bose glass regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-27T23:22:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cayley tree",
      "bose-einstein condensation",
      "dirty bosons",
      "algebraic vanishing bec density",
      "glass regime showing conventional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}