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Spin correlation functions and quasiparticle decay

We study one-dimensional anisotropic XXZ spin-$\frac12$ model with ferromagnetic sign of the coupling and $z-z$ exchange constant $J_z = ΔJ$, where $Δ< 1$, and $J$ is the coupling within XY spin plane. We calculate damping of low-energy excitations with $ω\ll T $ due to their scattering from thermal excitation bath with temperature $T \ll J$, taking into account nonzero curvature of the excitation spectrum, $ε(q) = u q + δε(q)$. We calculate also longitudinal spin-spin correlation function $\langle S^z(x,t)S^z(0,0) \rangle$ at $x \approx ut$ and find the shape of the spreading "wave packet".