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

TL;DR

This study investigates the spectral properties and critical behavior of Higgs and Goldstone mass gaps in the two-dimensional S=1 XY model using exact diagonalization, focusing on their finite-size scaling and amplitude ratios near the critical point.

Contribution

It provides detailed analysis of the Higgs and Goldstone excitations, especially near the critical point, with improved finite-size scaling methods and amplitude ratio evaluation.

Findings

Finite-size scaling behavior is improved with extended interaction parameters.

Critical amplitude ratio for Higgs and Goldstone mass gaps is analyzed.

Higgs excitation is embedded in the continuum of Goldstone modes.

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.