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arXiv · hep-th/0412191

Reduced qKZ equation and correlation functions of the XXZ model

H. Boos·M. Jimbo·T. Miwa·F. Smirnov·Y. Takeyama
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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 (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.

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H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama. 2005-04-12. Reduced qKZ equation and correlation functions of the XXZ model. https://doi.org/10.1007/s00220-005-1430-6

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