{
  "id": "1811.06241",
  "version": "v1",
  "published": "2018-11-15T09:05:52.000Z",
  "updated": "2018-11-15T09:05:52.000Z",
  "title": "Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions",
  "authors": [
    "Yoshihiro Nishiyama"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The quantum Ising chain with the interaction decaying as a power law $1/r^{1+\\sigma}$ of the distance between spins $r$ was investigated numerically. A particular attention was paid to the low-energy spectrum, namely, the single-magnon and two-magnon-bound-state masses, $m_{1,2}$, respectively, in the ordered phase. It is anticipated that for each $\\sigma$, the scaled bound-state mass $m_2/m_1$ should take a universal constant (critical amplitude ratio) in the vicinity of the critical point. In this paper, we calculated the amplitude ratio $m_2/m_1$ with the exact diagonalization method, which yields the spectral information such as $m_{1,2}$ directly. As a result, we found that the scaled mass $m_2/m_1$ exhibits a non-monotonic dependence on $\\sigma$; that is, the bound state is stabilized by an intermediate value of $\\sigma$. Such a feature is accordant with a recent observation based on the non-perturbative-renormalization-group method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-15T09:05:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum ising chain",
      "magnon-bound-state hierarchy",
      "long-range interactions",
      "criticality",
      "amplitude ratio"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}