Bethe vectors and recurrence relations for twisted Yangian based models

Abstract

We study Olshanski twisted Yangian based models, known as one-dimensional “soliton non-preserving” open spin chains, by means of algebraic Bethe Ansatz. The even case, when the bulk symmetry is gl 2n and the boundary symmetry is sp 2n or so 2n, was studied in [12]. In the present work, we focus on the odd case, when the bulk symmetry is gl 2n+1 and the boundary symmetry is so 2n+1. We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and Y(gl n)-type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.