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

TL;DR

This work analyzes how single-ion anisotropy $D$ affects the decay of transverse spin helices in antiferromagnetic spin-$S$ XXZ chains. Using iTEBD in the thermodynamic limit, the authors map the spatial structure onto a fixed helix wave number $Q$ and a single-time-vector observable, then compare numerical results with a spin-wave theory augmented by a finite-$D$ analysis. They find nontrivial, nonmonotonic decay patterns: for $S=1/2$ helices can be long-lived when the phantom condition $\cos(Q)=\Delta$ holds, while for larger $S$ the initial decay speeds up but can be slowed or even stabilized by appropriate $Q$ and negative or positive $D$, with long-time behavior influenced by DM interactions. The work introduces a SW-based stability criterion generalizing the phantom condition and highlights slow thermalization as a possible hallmark of perturbed quantum scars in these driven many-body systems.

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.

Figures (6)

• Figure 1: Time evolution of the spin-helix amplitude for $\Delta = 0$ and $D=0.5$.
• Figure 2: Same as Fig. \ref{['fig:color_Delta0']} but for $\Delta = 0.5$ and $D=0.5$.
• Figure 3: Spin-helix amplitude for $\Delta = 1.2$ and $D = \pm0.5$.
• Figure 4: Time evolution of the spin-helix amplitude for $S=1$ and $\theta = \pi/2$ near the wave number $Q$ with the slowest decay. Panel (a) and (b) are for parameters $(\Delta,D)=(0.5,0.5)$ and $(\Delta,D)=(1.2,-0.5)$, respectively. The inset in (a) displays $A(t)$ for $S=2$ using the same range for the axes.
• Figure 5: Difference between the phase velocity $v_\phi$ and the semiclassical prediction $v_\phi^{\rm sc}$\ref{['eq:SCS']}. The parameters are $S=1$, $\Delta = 0.5$ and $D=0.5$.