Algebraic aspects of the correlation functions of the integrable higher-spin XXZ spin chains with arbitrary entries

TL;DR

This paper explores algebraic properties of the higher-spin XXZ spin chain, focusing on correlation functions and elementary matrices, to facilitate the algebraic Bethe-ansatz derivation of multiple-integral representations.

Contribution

It introduces Hermitian conjugate vectors and Hermitian elementary matrices for the spin-s XXZ chain, advancing the algebraic framework for correlation function analysis.

Findings

Constructed Hermitian conjugate vectors in the massless regime

Introduced spin-s Hermitian elementary matrices

Enhanced algebraic Bethe-ansatz methods for correlation functions

Abstract

We discuss some fundamental properties of the XXZ spin chain, which are important in the algebraic Bethe-ansatz derivation for the multiple-integral representations of the spin-s XXZ correlation function with an arbitrary product of elementary matrices. For instance, we construct Hermitian conjugate vectors in the massless regime and introduce the spin-s Hermitian elementary matrices.