{
  "id": "1808.03585",
  "version": "v1",
  "published": "2018-08-10T15:20:13.000Z",
  "updated": "2018-08-10T15:20:13.000Z",
  "title": "One-dimensional quasicrystals with power-law hopping",
  "authors": [
    "X. Deng",
    "S. Ray",
    "S. Sinha",
    "G. V. Shlyapnikov",
    "L. Santos"
  ],
  "comment": "5 pages, 5 figures, plus Supplementary material",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.quant-gas",
    "cond-mat.stat-mech"
  ],
  "abstract": "One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $a\\leq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-10T15:20:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power-law hopping",
      "one-dimensional quasicrystals",
      "ergodic-to-multifractal edges",
      "long-range hops",
      "single-particle states undergo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}