By circumventing the difficulty of obtaining exact string state solutions to Bethe ansatz equations, we devise a truncated string-state-space approach for investigating spin dynamics in non-integrable spin-1/2 Heisenberg chain subjected to staggered field at various magnetization. The obtained dynamical spectra reveal a series of elastic peaks at integer multiples of the ordering wavevector $Q$, indicating the presence of multi-$Q$ Bethe string states within the ground state. The spectrum exhibits a separation between different string continua as the strength of the staggered field increases at low magnetization,reflecting the confinement of the Bethe strings. The approach has successfully provided a unified string-state-based picture for understanding spin dynamics observed in various phases of quasi-1D antiferromagnet $\rm YbAlO_3$ \cite{Yang_CBS_2023}, and also paves a way for investigating low-dimensional non-integrable systems.
Comment: 6 pages, 5 figures