Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 099, 12 pages      arXiv:1506.06550      https://doi.org/10.3842/SIGMA.2015.099

Slavnov and Gaudin-Korepin Formulas for Models without ${\rm U}(1)$ Symmetry: the Twisted XXX Chain

Samuel Belliard a and Rodrigo A. Pimenta bc
a) Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise, France
b) Departamento de Física, Universidade Federal de São Carlos, Caixa Postal 676, CEP 13565-905, São Carlos, Brasil
c) Physics Department, University of Miami, P.O. Box 248046, FL 33124, Coral Gables, USA

Received September 02, 2015, in final form December 02, 2015; Published online December 04, 2015

Abstract
We consider the XXX spin-$\frac{1}{2}$ Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without ${\rm U}(1)$ symmetry characterized by an inhomogenous Baxter T-Q equation.

Key words: algebraic Bethe ansatz; integrable spin chain; scalar product.

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