Contributor info: Dr Vidas Regelskis

Vidas Regelskis

SciPost Phys. 17, 126 (2024) · published 5 November 2024 | Toggle abstract · pdf

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.

Vidas Regelskis

SciPost Phys. 12, 067 (2022) · published 17 February 2022 | Toggle abstract · pdf

We present a supermatrix realisation of $q$-deformed spinor-spinor and spinor-vector $R$-matrices. These $R$-matrices are then used to construct transfer matrices for $U_{q^2}(\mathfrak{so}_{2n+1})$- and $U_{q}(\mathfrak{so}_{2n+2})$-symmetric closed spin chains. Their eigenvectors and eigenvalues are computed.