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

Abstract

We study the longitudinal dynamical structure factor $S^{zz}(q,ω)$ 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 $γ_q$ of the on-shell peak for $S^{zz}(q,ω)$. We use the Bethe ansatz to show that $γ_q\sim q^2$ for $q\ll 1$ and to calculate the amplitudes of the leading irrelevant operators in the effective field theory.

2 pages, 2 figures, proceedings SCES '07, Houston