Boson decay and the dynamical structure factor for the XXZ chain at finite magnetic field

We study the longitudinal dynamical structure factor $S^{zz}(q,\omega )$ for the anisotropic spin-1/2 (XXZ) chain at finite magnetic field using bosonization. The leading irrelevant operators in the effective bosonic model stemming from band curvature describe boson decay processes and lead to a high-frequency tail and a finite width ${\gamma }_q$ of the on-shell peak for $S^{zz}(q,\omega )$. We use the Bethe ansatz to show that ${\gamma }_q\sim q^2$ for $q\ll 1$ and to calculate the amplitudes of the leading irrelevant operators in the effective field theory.