Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections

TL;DR

This paper develops an exact solution method for the SU(3) quantum spin chain with generic off-diagonal boundary conditions using a generalized nested off-diagonal Bethe ansatz, fusion techniques, and functional analysis.

Contribution

It extends the nested off-diagonal Bethe ansatz to SU(3) chains with non-diagonal boundaries, deriving functional relations and Bethe ansatz equations.

Findings

Derived closed operator identities among fused transfer matrices.

Obtained nested inhomogeneous T-Q relations and Bethe ansatz equations.

Results can be generalized to SU(n) algebra cases.

Abstract

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T-Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the $SU_q(n)$ algebra.