N-point Correlation Functions of the Spin-1 XXZ Model

TL;DR

This paper derives explicit integral formulas for N-point correlation functions of the spin-1 XXZ model using a bosonic and fermionic realization of quantum affine algebra, simplifying previous approaches by avoiding screening charges.

Contribution

It extends Jimbo et al.'s method to the spin-1 XXZ model, providing integral formulas without screening charges, and realizes the symmetry algebra with a deformed bosonic and fermionic fields.

Findings

Correlation functions expressed as classical integrals

No screening charges or Jackson integrals needed

Realization of quantum affine symmetry algebra

Abstract

We extend the recent approach of M. Jimbo, K. Miki, T. Miwa, and A. Nakayashiki to derive an integral formula for the N-point correlation functions of arbitrary local operators of the antiferromagnetic spin-1 XXZ model. For this, we realize the quantum affine symmetry algebra $U_q(su(2)_2)$ of level 2 and its corresponding type I vertex operators in terms of a deformed bosonic field free of a background charge, and a deformed fermionic field. Up to GSO type projections, the Fock space is already irreducible and therefore no BRST projections are involved. This means that no screening charges with their Jackson integrals are required. Consequently, our N-point correlation functions are given in terms of usual classical integrals only, just as those derived by Jimbo et al in the case of the spin-1/2 XXZ model through the Frenkel-Jing bosonization of $U_q(su(2)_1)$.