Reduced qKZ equation and correlation functions of the XXZ model

Abstract

Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (\lambda_1,...,\lambda_{2n}) as (\lambda_1,...,\lambda_n,\lambda_{n}+1,...,\lambda_{1}+1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functions $\tilde{\omega}, \omega$ with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice of $\tilde{\omega}, \omega$. We also present a conjectural formula in the massless regime.