Bethe vectors and recurrence relations for twisted Yangian based models

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 [Ann. Henri Poincaré 20, 339 (2018)]. In the present work, we focus on the odd case, when the bulk symmetry is gl2n+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.