{
  "id": "2106.01965",
  "version": "v1",
  "published": "2021-06-03T16:12:55.000Z",
  "updated": "2021-06-03T16:12:55.000Z",
  "title": "Dynamical phases in a \"multifractal\" Rosenzweig-Porter model",
  "authors": [
    "I. M. Khaymovich",
    "V. E. Kravtsov"
  ],
  "comment": "19 pages, 8 figures, 72 references + 3 pages, 5 figures in Appendices",
  "categories": [
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We consider the static and dynamic phases in a Rosenzweig-Porter (RP) random matrix ensemble with the tailed distribution of off-diagonal matrix elements of the form of the large-deviation ansatz. We present a general theory of survival probability in such a random-matrix model and show that the {\\it averaged} survival probability may decay with time as the simple exponent, as the stretch-exponent and as a power-law or slower. Correspondingly, we identify the exponential, the stretch-exponential and the frozen-dynamics phases. As an example, we consider the mapping of the Anderson model on Random Regular Graph (RRG) onto the \"multifractal\" RP model and find exact values of the stretch-exponent $\\kappa$ depending on box-distributed disorder in the thermodynamic limit. As another example we consider the logarithmically-normal RP (LN-RP) random matrix ensemble and find analytically its phase diagram and the exponent $\\kappa$. In addition, our theory allows to compute the shift of apparent phase transition lines at a finite system size and show that in the case of RP associated with RRG and LN-RP with the same symmetry of distribution function of hopping, a finite-size multifractal \"phase\" emerges near the tricritical point which is also the point of localization transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-03T16:12:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rosenzweig-porter model",
      "dynamical phases",
      "multifractal",
      "random matrix ensemble",
      "apparent phase transition lines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}