Fusion and Analytical Bethe Ansatz for the $A_{\n-1}^{(1)}$ Open Spin Chain

TL;DR

This paper extends the fusion procedure and crossing symmetry analysis for the $A_{n-1}^{(1)}$ open spin chain and solves it using the analytical Bethe ansatz, confirming known results with a new approach.

Contribution

It introduces a generalized fusion procedure and crossing property for the $A_{n-1}^{(1)}$ open spin chain and applies the analytical Bethe ansatz to solve it.

Findings

Fusion procedure generalized for $A_{n-1}^{(1)}$

Transfer matrix satisfies crossing symmetry

Analytical Bethe ansatz solution matches nested Bethe ansatz results

Abstract

We generalise the fusion procedure for the $A_{\n-1}^{(1)}$ open spin chain ($\n>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\n-1}^{(1)}$ open spin chain with $U_{q} (SU(\n))$ symmetry by means of the analytical Bethe ansatz method. Our results coincide with the known ones obtained by means of the nested Bethe ansatz.