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

TL;DR

This paper investigates the dynamical structure factor of the XXZ spin chain at finite magnetic field, revealing how boson decay processes influence spectral features and quantifying the decay rate using Bethe ansatz.

Contribution

It introduces a bosonization approach incorporating band curvature effects to describe boson decay and calculates the decay rate and amplitudes using Bethe ansatz.

Findings

Decay rate scales as q^2 for small q

High-frequency tail in the structure factor is explained by boson decay

Amplitudes of irrelevant operators are explicitly calculated

Abstract

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.