Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity

TL;DR

This paper presents an exact Bethe-Ansatz solution for the open XXZ spin chain with arbitrary boundary conditions at roots of unity, expanding the understanding of integrable quantum spin systems.

Contribution

It introduces a generalized T-Q equation approach with multiple Q functions for the open XXZ chain with full boundary parameter generality at roots of unity.

Findings

Numerical evidence supports completeness of the solution.

Solution applies to arbitrary boundary parameters without constraints.

Provides a framework for exact eigenvalue determination in complex boundary conditions.

Abstract

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are arbitrary, and need not satisfy any constraint. The solution is in terms of generalized T - Q equations, having more than one Q function. We find numerical evidence that this solution gives the complete set of 2^N transfer matrix eigenvalues, where N is the number of spins.