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

TL;DR

This paper develops a nested algebraic Bethe ansatz method for open spin chains with even twisted Yangian symmetry, relating their spectral problem to that of $ ext{gl}_n$-symmetric periodic chains, and explicitly constructs Bethe vectors and equations.

Contribution

It introduces a generalized nested algebraic Bethe ansatz for open spin chains with twisted Yangian symmetry, connecting their spectral analysis to well-understood $ ext{gl}_n$ models.

Findings

Derived explicit Bethe vectors for the model.

Formulated nested Bethe equations for the system.

Established a relation to $ ext{gl}_n$-symmetric periodic chains.

Abstract

We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian $Y^\pm(\mathfrak{gl}_{2n})$. 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 Bethe vectors and the nested Bethe equations.