Higher spin polynomial solutions of quantum Knizhnik--Zamolodchikov equation

TL;DR

This paper derives explicit formulas for correlation functions of vertex operators in quantum affine algebra, connecting them to Macdonald polynomials, and applies these to analyze ground states of higher spin models at roots of unity.

Contribution

It provides new explicit formulae for correlation functions of higher spin vertex operators using Macdonald polynomials, advancing the understanding of quantum integrable models.

Findings

Explicit formulas for correlation functions at arbitrary integer level

Application to ground state computations of higher spin models

Connection between vertex operators and Macdonald polynomials

Abstract

We provide explicit formulae for highest-weight to highest-weight correlation functions of perfect vertex operators of $U_q(\hat{\mathfrak{sl}(2)})$ at arbitrary integer level $\ell$. They are given in terms of certain Macdonald polynomials. We apply this construction to the computation of the ground state of higher spin vertex models, spin chains (spin $\ell/2$ XXZ) or loop models in the root of unity case $q=-e^{-i\pi/(\ell+2)}$.