{
  "id": "1905.04622",
  "version": "v1",
  "published": "2019-05-12T01:44:55.000Z",
  "updated": "2019-05-12T01:44:55.000Z",
  "title": "Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps",
  "authors": [
    "Yoshihiro Nishiyama"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The quantum $XY$ spin chain with the interactions decaying as a power law $1/r^{1+ \\sigma}$ of the distance between spins $r$ was investigated with the exact diagonalization method. Here, the constituent spin is set to $S=1$, which enables us to incorporate the biquadratic interactions so as to realize the order-disorder transition with the O$(2)$ symmetry maintained. Thereby, in the ordered phase, we resolved the Higgs mass $m_H$ out of the Goldstone-excitation continuum by specifying Higgs-particle's quantum numbers to adequate indices. We then turn to the analysis of the critical amplitude ratio $m_H / \\Delta$ ($\\Delta$: paramagnetic gap in the disordered phase). As the power of the algebraic decay $\\sigma$ increases, the amplitude ratio $m_H/\\Delta$ gets enhanced gradually in agreement with the $\\epsilon(=4-D)$-expansion-renormalization-group result; here, we resort to the $\\sigma \\leftrightarrow D$ relation advocated recently in order to establish a relationship between the renormalization-group result and ours.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-12T01:44:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "amplitude ratio",
      "paramagnetic gap",
      "higgs mass",
      "long-range quantum",
      "criticality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}