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By circumventing the difficulty of obtaining exact string state solutions toBethe ansatz equations, we devise a truncated string-state-space approach forinvestigating spin dynamics in non-integrable spin-1/2 Heisenberg chainsubjected to staggered field at various magnetization. The obtained dynamicalspectra reveal a series of elastic peaks at integer multiples of the orderingwavevector $Q$, indicating the presence of multi-$Q$ Bethe string states withinthe ground state. The spectrum exhibits a separation between different stringcontinua as the strength of the staggered field increases at lowmagnetization,reflecting the confinement of the Bethe strings. The approach hassuccessfully provided a unified string-state-based picture for understandingspin dynamics observed in various phases of quasi-1D antiferromagnet $\rmYbAlO_3$ \cite{Yang_CBS_2023}, and also paves a way for investigatinglow-dimensional non-integrable systems.

Truncated string-state-space approach and its application to non-integrable spin 1/2 Heisenberg chain