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Journal of the Physical Society of Japan

Integral Solution of Trigonometric Knizhnik-Zamolodchikov Equation; Off-Shell Bethe Ansatz Method

Toshio Hasegawa, Kazuhiro Hikami, Miki Wadati

Published Aug 15, 1994• 9 citations
Publisher

Abstract

We construct the solutions of the s u (2) trigonometric Knizhnik-Zamolodchikov (KZ) equation based on the Babujian's "off-shell Bethe ansatz" method. We show that the quasi-classical limit of the Bethe ansatz equation including the "unwanted term" for the inhomogeneous XXZ lattice reduces to the trigonometric KZ equation.

DOI
10.1143/jpsj.63.2895

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We construct the solutions of the s u (2) trigonometric Knizhnik-Zamolodchikov (KZ) equation based on the Babujian's "off-shell Bethe ansatz" method. We show that the quasi-classical limit of the Bethe ansatz equation including the "unwanted term" for the inhomogeneous XXZ lattice reduces to the trigonometric KZ equation.
The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the corresponding Knizhnik–Zamolodchikov equations for the non-periodic sℓ(2) Gaudin model, as well as deriving the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, we provide a closed form expression also for the scalar products of the off-shell Bethe vectors. Finally, we provide explicit closed form of the off-shell Bethe vectors, together with a proof of implementation of the algebraic Bethe ansatz in full generality.