{
  "id": "1912.01406",
  "version": "v1",
  "published": "2019-12-03T14:29:57.000Z",
  "updated": "2019-12-03T14:29:57.000Z",
  "title": "Quantum Ising chains with small-world couplings: No small-world effect at the quantum level; Stability of the quantum critical point",
  "authors": [
    "Massimo Ostilli"
  ],
  "comment": "5 pages, 2 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "quant-ph"
  ],
  "abstract": "Due to the small-world effect, the critical behavior of finite dimensional classical systems of N spins is known to change radically when an O(N) number of couplings are randomly rewired or superimposed onto the original system. In particular, one-dimensional systems acquire a finite critical temperature while two-dimensional systems get higher critical temperatures and, in both cases, the critical behavior turns out to be mean-field like. Here, we prove that at the quantum level the above scenario does not apply: when an O(N) number of extra ferromagnetic couplings are randomly superimposed onto a quantum Ising chain, its quantum critical point and behavior remain both unchanged. In other words, at zero temperature quantum fluctuations destroy any small-world effect (quantum networks cannot be small-world). This exact result sheds new light on the significance of the quantum critical point as a thermodynamically stable feature of nature and might be crucial for quantum annealing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-03T14:29:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum critical point",
      "quantum ising chain",
      "small-world effect",
      "quantum level",
      "small-world couplings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}