Critical behavior of the Higgs- and Goldstone-mass gaps for the two-dimensional S=1 XY model

Abstract

Spectral properties for the two-dimensional quantum S=1 XY model were investigated with the exact diagonalization method. In the symmetry-broken phase, there appear the massive Higgs and massless Goldstone excitations, which correspond to the longitudinal and transverse modes of the spontaneous magnetic moment, respectively. The former excitation branch is embedded in the continuum of the latter, and little attention has been paid to the details, particularly, in proximity to the critical point. The finite-size-scaling behavior is improved by extending the interaction parameters. An analysis of the critical amplitude ratio for these mass gaps is made.

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Cited by in corpus (6)

• The nonperturbative functional renormalization group and its applications
• Universal scaled Higgs-mass gap for the bilayer Heisenberg model in the ordered phase
• Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Operator product expansion coefficients from the nonperturbative functional renormalization group