Non-diagonal reflection for the non-critical XXZ model

TL;DR

This paper derives the most general boundary S-matrix for the non-critical open XXZ spin chain using Bethe ansatz, expressing it with Gamma functions and reproducing known results in the isotropic limit.

Contribution

It provides a comprehensive derivation of the boundary S-matrix for the non-critical XXZ model, extending previous results and including the isotropic limit case.

Findings

Derived the boundary S-matrix in terms of Gamma functions

Reproduced known results for the open XXX chain

Extended understanding of boundary effects in non-critical XXZ models

Abstract

The most general physical boundary $S$-matrix for the open XXZ spin chain in the non-critical regime ($\cosh (\eta)>1$) is derived starting from the bare Bethe ansazt equations. The boundary $S$-matrix as expected is expressed in terms of $\Gamma_q$-functions. In the isotropic limit corresponding results for the open XXX chain are also reproduced.