On the particle excitations in the XXZ- spin chain

TL;DR

This paper investigates the excited states of the XXZ spin chain with complex Bethe roots, introduces a particle-hole symmetry, and explores the XXX spin chain limit and low-energy excitations.

Contribution

It proposes a novel particle-hole symmetry relating eigenstates from different pseudovacua and analyzes the XXX limit of complex roots in the XXZ chain.

Findings

Particle-hole symmetry relates different eigenstates.

Eigenstates with complex roots have a well-defined XXX limit.

Comments on low-energy excitations in the XXZ chain.

Abstract

We continue to study the excited states for the XXZ- spin chain corresponding to the complex roots of the Bethe Ansatz equations with the imaginary part equal to $\pi/2$. We propose the particle-hole symmetry which relates the eigenstates build up from the two different pseudovacuum states. We find the XXX- spin chain limit for the eigenstates with the complex roots. We also comment on the low-energy excited states for the XXZ- spin chain.