Universality in the relaxation of spin helices under XXZ spin-chain dynamics

We describe the dynamics of a transverse spin-helix state---a product state with spatially rotating magnetization---under XXZ spin chain evolution. Due to experimental relevance we especially focus on magnetization dynamics. At long times the $U(1)$ symmetry of the Hamiltonian is restored, leading to the decay of transverse magnetization, which can be described as an exponential decay of a spatially harmonic profile. We show that the dependence of the short- and intermediate-time decay timescale, which in principle depends on all different parameters, like the wave vector of the initial helix, the anisotropy, etc., can be described well by a single scaling function. We also briefly discuss the evolution of magnetization current.