Bethe vectors and recurrence relations for twisted Yangian based models

Publication date: 23 February 2023

Abstract: We study Olshanski twisted Yangian based models, known as one-dimensional "soliton non-preserving" open spin chains, by means of the algebraic Bethe ansatz. The even case, when the underlying bulk Lie algebra is $mathfrak{gl}_{2n}$, was studied in arXiv:1710.08409. In the present work, we focus on the odd case, when the underlying bulk Lie algebra is $mathfrak{gl}_{2n+1}$. We present a more symmetric form of the trace formula for Bethe vectors. 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.

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Exactly solvable models; Bethe ansatz (82B23)

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