arXiv:nlin/0105043 · International Journal of Modern Physics A

THE QUANTUM KNIZHNIK–ZAMOLODCHIKOV EQUATION ASSOCIATED WITH $U_q(A_2^{(2)})$ FOR |q| = 1

Takeo Kojima

Published Jan 16, 2003• 1 citation

Abstract

We present an integral representation to the quantum Knizhnik–Zamolodchikov equation associated with twisted affine symmetry [Formula: see text] for massless regime |q| = 1. Upon specialization, it leads to a conjectural formula for the correlation function of the Izergin–Korepin model in massless regime |q| = 1. In a limiting case q → -1, our conjectural formula reproduce the correlation function for the Izergin–Korepin model1,2 at critical point q = -1.

DOI: 10.1142/s0217751x0301214x

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arXiv:nlin/0105043 · International Journal of Modern Physics A

THE QUANTUM KNIZHNIK–ZAMOLODCHIKOV EQUATION ASSOCIATED WITH $U_q(A_2^{(2)})$ FOR |q| = 1THE QUANTUM KNIZHNIK–ZAMOLODCHIKOV EQUATION ASSOCIATED WITH $U_q(A_2^{(2)})$ FOR |q| = 1

Takeo Kojima

Published Jan 16, 2003• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.1142/s0217751x0301214x

Related papers

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Michio Jimbo, Tetsuji Miwa

arXiv:hep-th/9601135Journal of Physics A Mathematical and GeneralJun 21, 1996268 citations

The twisted quantum affine algebra Uq(A2(2)) and correlation functions of the Izergin-Korepin model

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THE QUANTUM KNIZHNIK–ZAMOLODCHIKOV EQUATION ASSOCIATED WITH

U_q(A_2^{(2)})

FOR |q| = 1

A bstract The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra U q (

{A}_2^{(2)}

A 2 2 ) symmetry. Applying the t - W method, we derive the homogeneous zeroes Bethe ansatz equations and the corresponding zeroes patterns of the Izergin-Korepin model with generic integrable boundaries. Based on these results, we analytically compute the surface energies and boundary excitations in different regimes of boundary parameters of the model. It is shown that in some regimes, correlation effect appears between two boundary fields.

\tfrac{1}{2}

in a magnetic field leads to multiple integral representations of its n-point correlation functions. For zero magnetic field, it gives a proof, in both the massless and massive (anti-ferromagnetic) regimes, of the formulas obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra

{\mathcal{U}_q}(\widehat s{l_2})

together with the corner transfer matrix approach (massive regime). We also discuss further problems, related in particular to long distance asymptotics of these correlation functions.