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 $\mathfrak{ gl}_{ 2n}$ and the boundary symmetry is $\mathfrak{ sp}_{ 2n}$ or $\mathfrak{ gl}_{ 2n}$, was studied in arXiv:1710.08409. In the present work, we focus on the odd case, when the bulk symmetry is $\mathfrak{ gl}_{ 2n+1}$ and the boundary symmetry is $\mathfrak{ so}_{ 2n+1}$. We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and $Y(\mathfrak{ gl}_n)$-type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.
Categories: math-ph hep-th math.MP nlin.SI