This article is cited in 10 papers

Scalar Products in Twisted XXX Spin Chain. Determinant Representation

Samuel Belliard^a, Nikita A. Slavnov<sup>b

a</sup> Institut Denis-Poisson, Université de Tours, Université d'Orléans, Parc de Grammont, 37200 Tours, France
^b Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Str., Moscow, 119991, Russia

Abstract: We consider XXX spin-$1/2$ Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors are on shell, we obtain a determinant representation for the norm of on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix.

Keywords: XXX chain, non-diagonal boundary conditions, scalar product, determinant.

MSC: 82B23, 81R50

Received: June 19, 2019; in final form August 27, 2019; Published online September 3, 2019

Language: English

DOI: 10.3842/SIGMA.2019.066

Bibliographic databases:

• 
• 
• 

ArXiv: 1906.06897