Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains

TL;DR

This paper develops a nested algebraic Bethe ansatz method for solving one-dimensional open spin chains with orthogonal and symplectic symmetry, extending previous techniques to more complex boundary conditions.

Contribution

It introduces a generalized nested Bethe ansatz for so(2n) and sp(2n) symmetric chains, relating their spectral problems to gl(n) chains, and explicitly constructs Bethe vectors and equations.

Findings

Derived explicit Bethe vectors for orthogonal and symplectic chains.

Established nested Bethe equations for these models.

Connected spectral problems to gl(n)-symmetric chains.

Abstract

We present a nested algebraic Bethe ansatz for one-dimensional open so(2n)- and sp(2n)-symmetric spin chains with diagonal boundary conditions and described by the extended twisted Yangian. We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so(2n)- or sp(2n)-symmetric open spin chain to that of a gl(n)-symmetric open spin chain. We explicitly derive the structure of Bethe vectors and the nested Bethe equations.