TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.5.126
TI  - Bethe vectors and recurrence relations for twisted Yangian based models
PY  - 2024/11/05
UR  - https://scipost.org/SciPostPhys.17.5.126
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 5
SP  - 126
A1  - Regelskis, Vidas
AB  - 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 $\mathfrak{so}_{2n}$, was studied in [Ann. Henri Poincaré 20, 339 (2018)]. In the present work, we focus on the odd case, when the bulk symmetry is $\mathfrak{gl}_{2n+1}$ 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.
ER  -

@Article{10.21468/SciPostPhys.17.5.126,
	title={{Bethe vectors and recurrence relations for twisted Yangian based models}},
	author={Vidas Regelskis},
	journal={SciPost Phys.},
	volume={17},
	pages={126},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.5.126},
	url={https://scipost.org/10.21468/SciPostPhys.17.5.126},
}