Quantized Delta S=2 Excitation Spectra by Confinement in an S=1 Spin Chain

We calculate the dynamical spin-structure factor of the $S=1$ Ising spin chain with negative single-ion anisotropy in magnetic fields using the infinite time-evolving-block-decimation algorithm. We show that when a transverse magnetic field is applied, both the $\Delta S=2$ excitation continuum and one-magnon mode appear in the low-lying excitation. When a longitudinal magnetic field is further applied, the excitation continuum changes into quantized excitation spectra. The quantized $\Delta S=2$ excitation spectra originate from the confinement of two domain walls, each of which carries $\Delta S=1$. The quantized excitation energies are explained by the negative zeros in the Airy function.