Criticality of the Higgs mass for the long-range quantum XY chain: Amplitude ratio between the Higgs and paramagnetic gaps

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Abstract

The quantum XY spin chain with the interactions decaying as a power law 1∕r1+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 mH 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 mH∕Δ (Δ: paramagnetic gap in the disordered phase). As the power of the algebraic decay σ increases, the amplitude ratio mH∕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 languageEnglish
Article number121395
JournalPhysica A: Statistical Mechanics and its Applications
Volume527
DOIs
Publication statusPublished - Aug 1 2019

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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