Bethe vectors and recurrence relations for twisted Yangian based models

Fuente: arXiv
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Main Author: Regelskis, Vidas
Format: Preprint
Published: 2023
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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