Confinement of many-body Bethe strings

TL;DR

This study investigates how the confinement of many-body Bethe strings in a quasi-one-dimensional antiferromagnet varies across different magnetic phases, revealing a transition from confined Bethe strings to conventional quantum physics with temperature changes.

Contribution

It provides the first comprehensive experimental and theoretical analysis of Bethe string confinement evolution in YbAlO3 across multiple magnetic phases.

Findings

Confined length-1 Bethe strings dominate in the antiferromagnetic phase.

Confined length-2 Bethe strings emerge in the spin-density-wave phase.

Confinement effects vanish in the thermal disordered region, restoring Heisenberg physics.

Abstract

Based on Bethe-ansatz approach and inelastic neutron scattering experiments, we reveal evolution of confinement of many-body Bethe strings in ordered regions of quasi-one-dimensional antiferromagnet $\rm YbAlO_3$. In the antiferromagnetic phase, the spin dynamics is dominated by the confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to the confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Our results establish a unified picture based on Bethe string for the spin dynamics in different magnetic phases of $\rm YbAlO_3$, and thus provide profound insight into the many-body quantum magnetism.