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 (λ_1,...,λ_{2n}) as (λ_1,...,λ_n,λ_{n}+1,...,λ_{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 $\tildeω, ω$ 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 $\tildeω, ω$. We also present a conjectural formula in the massless regime.