Bethe vectors and recurrence relations for twisted Yangian based models
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912050577408000 |
|---|---|
| author | Regelskis, Vidas |
| author_facet | Regelskis, Vidas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11842 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bethe vectors and recurrence relations for twisted Yangian based models Regelskis, Vidas Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 82B23 (Primary), 17B37 (Secondary) 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. |
| title | Bethe vectors and recurrence relations for twisted Yangian based models |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 82B23 (Primary), 17B37 (Secondary) |
| url | https://arxiv.org/abs/2302.11842 |