Quantized excitation spectra by magnon confinement in quasi-one-dimensional S=1 spin systems

We apply the infinite time-evolving-block-decimation algorithm to calculate the dynamical spin-structure factors of the quasi-one-dimensional (q1D) S=1 antiferromagnetic spin system with the single-ion anisotropy and the bond alternation. We find that excitation continuum originating from magnons is quantized, when the staggered field induced by the weak inter-chain interaction is taken into account. The excitation energies of the quantized excitation spectra are well explained by negative zeros of the Airy functions, when the easy-axis anisotropy is strong and the ground state is located deep in the N\'eel phase. This quantization of the magnon continuum is a counterpart of the spinon confinement, which has been recently discussed in q1D S=1/2 antiferromagnets. We further show that, when the staggered field exists, the quantized excitation spectra appear the phase boundary between the Haldane phase and the N\'eel phase of the phase diagram without the staggered field. However, the quantized excitation spectra disappear in the singlet dimer phase.