### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

### Cite this

**Criticality of the Higgs mass for the long-range quantum XY chain : Amplitude ratio between the Higgs and paramagnetic gaps.** / Nishiyama, Yoshihiro.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Criticality of the Higgs mass for the long-range quantum XY chain

T2 - Amplitude ratio between the Higgs and paramagnetic gaps

AU - Nishiyama, Yoshihiro

PY - 2019/8/1

Y1 - 2019/8/1

N2 - 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.

AB - 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.

KW - Critical amplitude ratio

KW - Critical exponent

KW - Long-range interactions

KW - Quantum XY spin model

UR - http://www.scopus.com/inward/record.url?scp=85065399931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065399931&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2019.121395

DO - 10.1016/j.physa.2019.121395

M3 - Article

AN - SCOPUS:85065399931

VL - 527

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

M1 - 121395

ER -