Quantized magnon-excitation continuum in quasi one-dimensional antiferromagnetic S=1 Heisenberg systems

In recent inelastic neutron scattering measurements on (Ba/Sr)Co₂V₂O₈[1,2], quantization of spinon-excitation continuum has been observed below the Néel temperature. The interesting point is that the excitation energies of the quantized spectra are well explained by negative zeros of the Airy functions (NZAF)[3]. In this study, we investigate the possibility of quantized magnon-excitation continuum in quasi-one-dimensional antiferromagnetic S=1 Heisenberg chains with the single-ion anisotropy, D. We use the infinite time-evolving-block-decimation method to compute dynamical spin structure factors and show that the magnon-excitation continuum is also quantized by the weak inter-chain interaction[4]. We find that the excitation energies agree with NZAF when D is quite large negatively. Although the quantization spectra survive up to D ~ 0, the excitation energies deviate from NZAF. [1] Z. Wang, et al., PRB 91, 140404(R) (2015). [2] B. Grenier, et al., PRL 114, 017201 (2015). [3] H. Shiba, Prog. Theor. Phys. 64, 466 (1980). [4] T. Suzuki, and S. Suga, arXiv:1808.06270.