Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry

Allan Gerrard, Niall MacKay, Vidas Regelskis

Published 2017-10-23Version 1

We present the nested algebraic Bethe ansatz for a one-dimensional open spin chain whose underlying symmetry is Olshanskii twisted Yangian $Y^\pm(\mathfrak{gl}_{2n})$, the Lie subalgebras of which are $\mathfrak{so}_{2n}$ or $\mathfrak{sp}_{2n}$. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-symmetric open spin chain to that of a $\mathfrak{gl}_n$-symmetric periodic spin chain. We explicitly derive the structure of the eigenvectors and the nested Bethe equations.