{
  "id": "1803.09756",
  "version": "v2",
  "published": "2018-03-26T18:00:01.000Z",
  "updated": "2018-10-08T16:57:23.000Z",
  "title": "Non-power-law universality in one-dimensional quasicrystals",
  "authors": [
    "Attila Szabó",
    "Ulrich Schneider"
  ],
  "comment": "18 pages, 13 figures",
  "journal": "Phys. Rev. B 98, 134201 (2018)",
  "doi": "10.1103/PhysRevB.98.134201",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.quant-gas",
    "cond-mat.stat-mech",
    "physics.atom-ph",
    "quant-ph"
  ],
  "abstract": "We have investigated scaling properties of the Aubry-Andr\\'e model and related one-dimensional quasiperiodic Hamiltonians near their localisation transitions. We find numerically that the scaling of characteristic energies near the ground state, usually captured by a single dynamical exponent, does not obey a power law relation. Instead, the scaling behaviour depends strongly on the correlation length in a manner governed by the continued fraction expansion of the irrational number $\\beta$ describing incommensurability in the system. This dependence is, however, found to be universal between a range of models sharing the same value of $\\beta$. For the Aubry-Andr\\'e model, we explain this behaviour in terms of a discrete renormalisation group protocol which predicts rich critical behaviour. This result is complemented by studies of the expansion dynamics of a wave packet under the Aubry-Andr\\'e model at the critical point. Anomalous diffusion exponents are derived in terms of multifractal (R\\'enyi) dimensions of the critical spectrum; non-power-law universality similar to that found in ground state dynamics is observed between a range of critical tight-binding Hamiltonians.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-10-08T16:57:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional quasicrystals",
      "aubry-andre model",
      "discrete renormalisation group protocol",
      "predicts rich critical behaviour",
      "non-power-law universality similar"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}