Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain

Abstract

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-$\frac{1}{2}$ 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 $\mathrm{YbAl}{\mathrm{O}}_3$.

12 pages, 6 figures

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Cited by in corpus (2)

• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory
• Spin-$s$ $Q$-systems: Twist and Open Boundaries