Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms

TL;DR

This paper develops a generalized T-Q relation for the open spin-s XXZ chain with nondiagonal boundaries at roots of unity, enabling Bethe-ansatz solutions and demonstrating their completeness through numerical checks.

Contribution

It introduces a new generalized T-Q relation involving multiple Q-functions for the open spin-s XXZ chain with nondiagonal boundary terms at roots of unity.

Findings

Derived a generalized T-Q relation for the model.

Proposed Bethe-ansatz-type eigenvalue expressions.

Numerical evidence supports the completeness of solutions.

Abstract

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which we use to propose the Bethe-ansatz-type expressions for the eigenvalues of the transfer matrix. At most two of the boundary parameters are set to be arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2, i\pi/4,... We also provide numerical evidence for the completeness of the Bethe-ansatz-type solutions derived, using s = 1 case as an example.