Bethe ansatz solution of the $\tau_2$-model with arbitrary boundary fields

TL;DR

This paper solves the quantum $ au_2$-model with arbitrary boundary fields using the off-diagonal Bethe Ansatz, providing eigenvalues, Bethe equations, and a novel inhomogeneous T-Q relation for models with site-dependent inhomogeneity.

Contribution

It introduces a new solution method for the $ au_2$-model with arbitrary boundary conditions, extending the applicability of Bethe Ansatz techniques.

Findings

Eigenvalues expressed via inhomogeneous T-Q relation

Derived Bethe Ansatz equations for the model

Applicable to models with site-dependent inhomogeneity

Abstract

The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T-Q relation, which is based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices. Moreover, the associated Bethe Ansatz equations are also obtained.