Generalized coordinate Bethe ansatz for non diagonal boundaries

TL;DR

This paper develops a generalized coordinate Bethe ansatz to solve the spectrum and eigenstates of the open XXX model with non-diagonal boundary matrices, where traditional methods fail due to boundary complexity.

Contribution

It introduces a novel generalized Bethe ansatz approach to handle non-diagonal boundary conditions in the open XXX model, expanding solvable cases.

Findings

Successfully computed the spectrum and eigenstates for the model

Extended Bethe ansatz method to non-diagonal boundary matrices

Provided analytical solutions where standard methods do not apply

Abstract

We compute the spectrum and the eigenstates of the open XXX model with non-diagonal (triangular) boundary matrices. Since the boundary matrices are not diagonal, the usual coordinate Bethe ansatz does not work anymore, and we use a generalization of it to solve the problem.