The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain

TL;DR

This paper computes the exact two-spinon contribution to the transverse dynamical structure factor of the gapped anisotropic Heisenberg spin-1/2 chain at zero field, revealing its asymmetry, anisotropy dependence, and sum rule contributions.

Contribution

It provides the first exact calculation of the two-spinon part of the transverse structure factor in the gapped XXZ model using integrability methods.

Findings

The two-spinon contribution shows asymmetry around the $rac{}$ momentum line.

The structure factor's anisotropy dependence is characterized.

Sum rule contributions of the two-spinon part are quantified.

Abstract

We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime ($\Delta > 1$). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the $\pi/2$ momentum line, its overall anisotropy dependence, and its contribution to sum rules.