Universal Berezinskii-Kosterlitz-Thouless dynamic scaling in the intermediate timerange in frustrated Heisenberg antiferromagnets on triangular lattice

TL;DR

This paper reveals that frustrated Heisenberg antiferromagnets on a triangular lattice exhibit universal BKT-like dynamic scaling in an intermediate time range, linked to $ ext{Z}_2$-vortex unbinding, similar to the 2D XY model.

Contribution

It demonstrates that the non-equilibrium dynamics of frustrated Heisenberg antiferromagnets show BKT-like scaling behavior in an intermediate time window, highlighting the role of $ ext{Z}_2$-vortices.

Findings

Dynamic transition at $T_u=0.282 J$ due to $ ext{Z}_2$-vortex unbinding.

Intermediate time range exhibits XY model-like behavior below BKT transition.

Long-time dynamics involve interaction of $ ext{Z}_2$-vortices with spin waves.

Abstract

We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are similar to those of two-dimensional XY model below Berezinskii-Kosterlitz-Thouless transition. The interaction of $\mathbb{Z}_2$-vortices with spin-wave degrees of freedom does not emerge until rather long times.