Factorization identities and algebraic Bethe ansatz for $D^{(2)}_{2}$ models

TL;DR

This paper derives factorization identities expressing $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ matrices, enabling algebraic Bethe ansatz solutions for new integrable spin chains with boundary parameters.

Contribution

It introduces factorization identities for $D^{(2)}_{2}$ models and applies them to solve new boundary-dependent integrable spin chains using algebraic Bethe ansatz.

Findings

Derived factorization identities for transfer matrices.

Solved a new XXZ-like open spin chain with boundary rapidity.

Extended algebraic Bethe ansatz methods to boundary-dependent models.

Abstract

We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like open spin chain with an even number of sites that depends on a continuous parameter, which we interpret as the rapidity of the boundary.