Truncated string state space approach and its application to the nonintegrable spin- 12 Heisenberg chain

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 a nonintegrable spin-1/2 Heisenberg chain subjected to a staggered field at various magnetizations. The obtained dynamical spectra reveal a series of elastic peaks at integer multiples of the ordering wave vector 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. This approach provides a unified string-state-based framework for understanding spin dynamics in low-dimensional nonintegrable Heisenberg models, which has a successful application to observations across various phases of the quasi-one-dimensional antiferromagnet YbAlO₃.