Spin correlation functions and quasiparticle decay

TL;DR

This paper investigates the decay and correlation functions of low-energy excitations in a one-dimensional anisotropic XXZ spin-1/2 model, accounting for spectrum curvature and thermal effects, providing insights into quasiparticle dynamics.

Contribution

It introduces a detailed calculation of quasiparticle damping and spin correlation functions in the XXZ model considering spectrum curvature and finite temperature effects.

Findings

Calculated damping rates of low-energy excitations due to thermal scattering.

Derived the shape and spreading of the spin correlation wave packet.

Analyzed the impact of spectrum curvature on quasiparticle decay.

Abstract

We study one-dimensional anisotropic XXZ spin-$\frac12$ model with ferromagnetic sign of the coupling and $z-z$ exchange constant $J_z = \Delta J$, where $\Delta < 1$, and $J$ is the coupling within XY spin plane. We calculate damping of low-energy excitations with $\omega \ll T $ due to their scattering from thermal excitation bath with temperature $T \ll J$, taking into account nonzero curvature of the excitation spectrum, $\epsilon(q) = u q + \delta\epsilon(q)$. 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".