Samuel Belliard, Rodrigo A. Pimenta, “Slavnov and Gaudin–Korepin Formulas for Models without <nobr>$\mathrm{U}(1)$</nobr> Symmetry: the Twisted XXX Chain”, SIGMA, 2015, Volume 11,099, 12 pp.

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

Samuel Belliard^a, 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

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 $\mathrm{U}(1)$ symmetry characterized by an inhomogenous Baxter T-Q equation.

Keywords: algebraic Bethe ansatz; integrable spin chain; scalar product.

MSC: 82B23; 81R12

Received: September 2, 2015; in final form December 2, 2015; Published online December 4, 2015

Language: English

DOI: 10.3842/SIGMA.2015.099