### Abstract

The quantum XY spin chain with the interactions decaying as a power law 1∕r
^{1+σ}
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}
∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio m
_{H}
∕Δ gets enhanced gradually in agreement with the ϵ(=4−D)-expansion-renormalization-group result; here, we resort to the σ↔D relation advocated recently in order to establish a relationship between the renormalization-group result and ours.

Original language | English |
---|---|

Article number | 121395 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 527 |

DOIs | |

Publication status | Published - Aug 1 2019 |

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### Keywords

- Critical amplitude ratio
- Critical exponent
- Long-range interactions
- Quantum XY spin model

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics