Reduced QKZ equation and correlation functions of the XXZ model

Dec, 2004
32 pages
Published in:
  • Commun.Math.Phys. 261 (2006) 245-276
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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 ω~,ω\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 ω~,ω\tilde{\omega}, \omega. We also present a conjectural formula in the massless regime.
Note:
  • 32 pages, some formulas revised