Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

TL;DR

This paper develops a comprehensive nested Bethe ansatz framework for open spin chains with various algebraic structures and diagonal boundary conditions, unifying and extending previous results.

Contribution

It provides a unified, detailed construction of the nested Bethe ansatz for a broad class of open spin chains with arbitrary representations and diagonal boundaries.

Findings

Eigenvalues and Bethe equations derived for the models.

Bethe vectors expressed via a trace formula.

Extension and unification of previous Bethe ansatz results.

Abstract

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices (K^+(u),K^-(u)). The nested Bethe anstaz applies for a general K^-(u), but a particular form of the K^+(u) matrix. The construction extends and unifies the results already obtained for open spin chains based on fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.