Year: 2024
Type: article
Abstract: 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} 𝔤 𝔩 2 n and the boundary symmetry is \mathfrak{sp}_{2n} 𝔰 𝔭 2 n or \mathfrak{so}_{2n} 𝔰 𝔬 2 n , 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} 𝔤 𝔩 2 n + 1 and the boundary symmetry is \mathfrak{so}_{2n+1} 𝔰 𝔬 2 n + 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) Y ( 𝔤 𝔩 n ) -type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.
Source: SciPost Physics
Author: Vidas Regelskis
Institutions: University of Hertfordshire, Vilnius University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404082602