Exact solution of the quantum integrable model associated with the twisted $D^{(2)}_3$ algebra

TL;DR

This paper develops an exact solution method for the quantum integrable model related to the twisted D^{(2)}_3 algebra, providing explicit eigenvalues and Bethe ansatz equations for both periodic and open boundary conditions.

Contribution

It extends the nested off-diagonal Bethe ansatz method to the D^{(2)}_3 model, deriving eigenvalues and Bethe ansatz equations for arbitrary anisotropic parameters.

Findings

Eigenvalues expressed via homogeneous and inhomogeneous T-Q relations

Bethe ansatz equations derived for both periodic and open cases

Method generalizable to higher rank D^{(2)}_{n+1} models

Abstract

We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter $\eta$. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous $T-Q$ relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the $D^{(2)}_{n+1}$ model and other high rank integrable models.