Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with \eta=i\pi/3

TL;DR

This paper analyzes the elementary excitations and their scattering matrix in the thermodynamic limit of the antiperiodic XXZ spin chain at a specific anisotropic parameter, revealing detailed excitation patterns and interactions.

Contribution

It introduces a zero-point parameterization of transfer matrix eigenvalues and derives the scattering matrix for elementary excitations in this model.

Findings

Patterns of zero point distribution identified

Ground state energy calculated

Two-body scattering matrix obtained

Abstract

We study the thermodynamic limit of the antiperiodic XXZ spin chain with the anisotropic parameter $\eta=\frac{\pi i}{3}$. We parameterize eigenvalues of the transfer matrix by their zero points instead of Bethe roots. We obtain patterns of the distribution of zero points. Based on them, we calculate the ground state energy and the elementary excitations in the thermodynamic limit. We also obtain the two-body scattering matrix of elementary excitations. Two types of elementary excitations and three types of scattering processes are discussed in detailed.