Simplified Calculation of Boundary S Matrices

TL;DR

This paper presents a simplified derivation of the boundary S matrix for the open antiferromagnetic spin-1/2 Heisenberg chain with diagonal boundary fields, focusing on the odd excitation sector.

Contribution

It introduces a new simplified method leveraging the single excitation state in the odd sector to derive the boundary S matrix.

Findings

Derived explicit boundary S matrix expressions

Simplified the calculation process compared to previous methods

Confirmed consistency with known results

Abstract

The antiferromagnetic Heisenberg spin chain with N spins has a sector with N=odd, in which the number of excitations is odd. In particular, there is a state with a single one-particle excitation. We exploit this fact to give a simplified derivation of the boundary S matrix for the open antiferromagnetic spin-1/2 Heisenberg spin chain with diagonal boundary magnetic fields.