Universal scaled Higgs-mass gap for the bilayer Heisenberg model in the ordered phase

TL;DR

This study investigates the universal scaled Higgs mass in the ordered phase of the bilayer Heisenberg model using numerical diagonalization, confirming its universality near the critical point.

Contribution

It provides a finite-size-scaling analysis of the Higgs mass, demonstrating its universality in the bilayer Heisenberg model close to criticality.

Findings

Universal scaled Higgs mass estimated near the critical point

Finite-size scaling confirms universality of the Higgs mass

Spectral analysis isolates Higgs excitation from Goldstone modes

Abstract

The spectral properties for the bilayer quantum Heisenberg model were investigated with the numerical diagonalization method. In the ordered phase, there appears the massive Higgs excitation embedded in the continuum of the Goldstone excitations. Recently, it was claimed that the properly scaled Higgs mass is a universal constant in proximity to the critical point. Diagonalizing the finite-size cluster with $N \le 36$ spins, we calculated the dynamical scalar susceptibility $\chi_s"(\omega)$, which is rather insensitive to the Goldstone mode. A finite-size-scaling analysis of $\chi_s "(\omega)$ is made, and the universal (properly scaled) Higgs mass is estimated.