Direct Calculation of the Boundary $S$ Matrix for the Open Heisenberg Chain

TL;DR

This paper computes the boundary S matrix for the open Heisenberg spin chain with boundary magnetic fields using Bethe Ansatz, extending existing methods and confirming consistency with boundary sine-Gordon model results.

Contribution

It introduces a method to directly calculate the boundary S matrix for the open Heisenberg chain from Bethe Ansatz solutions, aligning with known boundary sine-Gordon results.

Findings

Boundary S matrix matches boundary sine-Gordon model with  boundary conditions

Method extends Korepin-Andrei-Destri approach to new boundary conditions

Results confirm theoretical predictions for boundary integrable models

Abstract

We calculate the boundary $S$ matrix for the open antiferromagnetic spin $1/2$ isotropic Heisenberg chain with boundary magnetic fields. Our approach, which starts from the model's Bethe Ansatz solution, is an extension of the Korepin-Andrei-Destri method. Our result agrees with the boundary $S$ matrix for the boundary sine-Gordon model with $\beta^2 \rightarrow 8\pi$ and with ``fixed'' boundary conditions.