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 ${\mathfrak{gl}}_{2n}$ 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.

39 pages. v2: introduction and conclusions extended, appendix added, minor updates to the main parts, submission to SciPost Physics. v3: notation updated