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arXiv:hep-th/9408135 · Journal of Physics A Mathematical and General

Functional relations and analytic Bethe ansatz for twisted quantum affine algebras

A Kuniba, J Suzuki

Published Feb 7, 1995• 38 citations
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Abstract

Functional relations are proposed for transfer matrices of solvable vertex models associated with the twisted quantum affine algebras U q (X n ( kappa ) ), where X n ( kappa ) =A n (2) , D n (2) , E 6 (2) and D 4 (3) . Their solutions are obtained for A n (2) and conjectured for D 4 (3) in the dressed vacuum form of the analytic Bethe ansatz.

DOI
10.1088/0305-4470/28/3/024

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On Bethe Ansatz for a Supersymmetric Vertex Model with Uq[osp(2∣2)(2)]\mathcal{U}_{\rm q}[{\rm osp}(2|2)^{(2)}]Uq​[osp(2∣2)(2)]
The Algebraic Bethe ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra Uq[osp(2∣2)(2)]\mathcal{U}_{q}[\mathrm{osp}(2|2)^{(2)}]Uq​[osp(2∣2)(2)] is presented in detail. The eigenvalues and eigenvectors of the row-to-row transfer matrix are calculated and the corresponding Bethe Ansatz equations are obtained and analyzed numerically.
An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is found. A complete set of transfer matrix functional relations (T-system) is proposed as a reduction of a Hirota-Miwa equation. We also derive a thermodynamic Bethe ansatz (TBA) equation from this T-system and the quantum transfer matrix method. This TBA equation is identical to the one from the string hypothesis.