We study the 19-vertex model associated with the quantum group [Formula: see text] at critical regime |q|=1. We give the realizations of the vertex operators in terms of free bosons and free fermions. Using these free field realizations, we present integral representations for the correlation functions.
LEVEL 2 IRREDUCIBLE REPRESENTATIONS OF Uq(sl2), VERTEX OPERATORS, AND THEIR CORRELATIONS
Starting from the finite volume form factors of local operators, we show how and under which hypothesis the c = 1 free boson conformal field theory in two-dimensions emerges as an effective theory governing the large-distance regime of multi-point correlation functions for a large class of one-dimensional massless quantum Hamiltonians. In our approach, in the large-distance critical regime, the local operators of the initial model are represented by well suited vertex operators associated to the free boson model. This provides an effective field theoretic description of the large distance behaviour of correlation functions in 1D quantum critical models. We develop this description starting from the first principles and directly at the microscopic level, namely in terms of the properties of the finite volume matrix elements of local operators.
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).