Off-diagonal Bethe Ansatz for the $D^{(1)}_3$ model

TL;DR

This paper develops an off-diagonal Bethe Ansatz method to exactly solve the $D^{(1)}_3$ quantum spin chain with various boundary conditions, providing a framework that can be extended to higher models.

Contribution

It introduces a novel off-diagonal Bethe Ansatz approach for the $D^{(1)}_3$ model, including complete operator identities and $T-Q$ relations for different boundary conditions.

Findings

Derived the spectrum using fusion and operator identities.

Constructed eigenvalues via $T-Q$ relations for periodic and open boundaries.

Method can be generalized to $D^{(1)}_{n}$ models.

Abstract

The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the $T-Q$ relations for the periodic case and by the inhomogeneous $T-Q$ one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the $D^{(1)}_{n}$ model directly.