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

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.