Bethe ansatz of the open spin-s XXZ chain with nondiagonal boundary terms

TL;DR

This paper develops a Bethe ansatz solution for the open spin-s XXZ chain with nondiagonal boundary conditions at specific anisotropy values, providing a new analytical approach and numerical validation for certain boundary parameter cases.

Contribution

It introduces a Bethe ansatz method for the open spin-s XXZ chain with nondiagonal boundaries at roots of unity, expanding solvable cases beyond previous diagonal boundary solutions.

Findings

Bethe ansatz solutions derived for specific boundary parameters

Numerical evidence supports completeness of solutions for s=1/2 and s=1

Analytical framework at roots of unity for certain anisotropy values

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 propose the Bethe ansatz solution for the transfer matrix eigenvalues for cases where atmost two of the boundary parameters are set to be arbitrary and the bulk anisotropy parameter has values \eta = i \pi/3, i \pi/5,... We present numerical evidence to demonstrate completeness of the Bethe ansatz solutions derived for s = 1/2 and s = 1.