Bethe vectors and recurrence relations for twisted Yangian based models

Abstract

We study Olshanski twisted Yangian based models, known as one-dimensional "soliton nonpreserving" open spin chains, by means of the algebraic Bethe ansatz. The even case, when the underlying bulk Lie algebra is gl 2n , was studied in [GMR19]. In the present work, we focus on the odd case, when the underlying bulk Lie algebra is gl 2n+1 . We present a more symmetric form of the trace formula for Bethe vectors. 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.