N-point correlation functions of the spin-1 XXZ model

Abstract

We extend the recent approach of Jimbo, Miki, Miwa and 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) .