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

TL;DR

This paper introduces a truncated string state space method to analyze spin dynamics in a nonintegrable Heisenberg chain with a staggered field, revealing multi-Q Bethe string states and string confinement effects.

Contribution

It develops a novel truncated string state space approach that circumvents solving Bethe ansatz equations exactly, enabling analysis of spin dynamics in nonintegrable models.

Findings

Detection of elastic peaks at multiples of the ordering wave vector Q

Observation of string confinement effects with increasing staggered field

Application to experimental data on YbAlO3

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 $\rm YbAlO_3$.