Decay of spin helices in XXZ quantum spin chains with single-ion anisotropy

TL;DR

This paper investigates the decay dynamics of spin-helix states in XXZ quantum spin chains with single-ion anisotropy, revealing conditions for their stability and longevity through numerical and analytical methods.

Contribution

It provides a combined numerical and analytical study of spin-helix decay in XXZ chains with single-ion anisotropy, highlighting stability conditions for these states.

Findings

Spin-helix states can be long-lived for specific wave numbers.

Single-ion anisotropy can stabilize helices, especially with easy-axis anisotropy.

A spin-wave approximation estimates the most stable wave number Q.

Abstract

Long-lived spin-helix states facilitate the study of non-equilibrium dynamics in quantum magnets. We consider the decay of transverse spin-helices in antiferromagnetic spin-$S$ XXZ chains with single-ion anisostropy. The spin-helix decay is observable in the time evolution of the local magnetization that we calculate numerically for the system in the thermodynamic limit using infinite time-evolving block decimation simulations. Although the single-ion anisotropy prevents helix states from being eigenstates of the Hamiltonian, they still can be long-lived for appropriately chosen wave numbers. In case of an easy-axis exchange anisotropy the single-ion anisotropy may even stabilize the helices. Within a spin-wave approximation, we obtain a condition giving an estimate for the most stable wave number $Q$ that agrees qualitatively with our numerical results.