Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain

TL;DR

This paper applies the algebraic Bethe ansatz to solve the eigenvalue problem of the spin-1 Temperley-Lieb quantum chain with open boundaries, providing explicit eigenvalues and eigenvectors.

Contribution

It introduces a method to derive eigenvalues and eigenvectors for the spin-1 Temperley-Lieb chain using reflection algebra techniques.

Findings

Eigenvalues of the spin-1 Temperley-Lieb chain obtained

Explicit eigenvectors constructed via algebraic Bethe ansatz

Off-shell equations for Bethe vectors proved

Abstract

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell equation satisfied by the Bethe vectors.