Confinement of many-body Bethe strings

Based on Bethe-ansatz approach and inelastic neutron scattering experiments, we reveal evolution of confinement of many-body Bethe strings in ordered regions of quasi-one-dimensional antiferromagnet $\rm YbAlO_3$. In the antiferromagnetic phase, the spin dynamics is dominated by the confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to the confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Our results establish a unified picture based on Bethe string for the spin dynamics in different magnetic phases of $\rm YbAlO_3$, and thus provide profound insight into the many-body quantum magnetism.