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
Uq(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
Uq(su(2)1).
In this paper we study nearest-neighbour deformations of integrable models. After expanding in the deformation parameter, we identify four possible types of deformations. First there are deformations that simply break or preserve integrability. Then we find two different subtle cases. The first case is where the deformation is only integrable if all orders of the deformation parameter are taken into account. An example of these are the long-range deformations that appear in holographic models. The second case is when the deformation is perturbatively integrable to some order in the deformation parameter but can not be extended to an integrable model. In this paper we work this out for the XXZ spin chain and discuss the level statistics of each of these cases. We find numerical evidence that the onset of chaos occurs differently in each of these models. For the perturbatively integrable models, we find that the deformation strength at which chaos appears demonstrates a volume-scaling intermediate between strong and weak integrability breaking models.