Spinon dynamics in quantum integrable antiferromagnets

TL;DR

This paper investigates the real-space dynamics of spinons in quantum antiferromagnetic chains, revealing their propagation as domain walls and their correlation spreading within a Lieb-Robinson light cone, using algebraic Bethe ansatz.

Contribution

It provides a detailed real-time visualization of spinon propagation in integrable models using algebraic Bethe ansatz, highlighting anisotropy effects and correlation dynamics.

Findings

Spinons propagate as domain walls in antiferromagnetic chains.

Correlation spreading follows a light cone consistent with Lieb-Robinson bounds.

Anisotropy influences spinon behavior and correlation dynamics.

Abstract

The excitations of the Heisenberg antiferromagnetic spin chain in zero field are known as spinons. As pairwise-created fractionalized excitations, spinons are important in the understanding of inelastic neutron scattering experiments in (quasi) one-dimensional materials. In the present work, we consider the real space-time dynamics of spinons originating from a local spin flip on the antiferromagnetic ground state of the (an)isotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model. By utilizing algebraic Bethe ansatz methods at finite system size to compute the expectation value of the local magnetization and spin-spin correlations, spinons are visualized as propagating domain walls in the antiferromagnetic spin ordering with anisotropy dependent behavior. The spin-spin correlation after the spin flip displays a light cone, satisfying the Lieb-Robinson bound for the propagation of correlations at the spinon velocity.