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arXiv:hep-th/9407089 · Journal of Physics A Mathematical and General

Direct calculation of the boundary S-matrix for the open Heisenberg chain

M.T. Grisaru, L Mezincescu, R I Nepomechie

Published Feb 21, 1995• 40 citations
arXivHTMLPDF

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 to 8 pi and with 'fixed' boundary conditions.

DOI
10.1088/0305-4470/28/4/025

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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 to 8 pi and with 'fixed' boundary conditions.
We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which generalizes these results. We first consider an integrable alternating spin 1/2 - spin 1 chain. In addition to having excitations with spin 1/2, this model also has excitations with spin 0. We compute the bulk S matrix, which has some unusual features. We then consider the open antiferromagnetic spin 1/2 Heisenberg chain with boundary magnetic fields. We give a direct calculation of the boundary S matrix. (Talk presented at the conference on Statistical Mechanics and Quantum Field Theory at USC, 16 - 21 May 1994)
We derived the corresponding boundary condition on Fermi fields to the spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the correct boundary condition from the variation of the action at the edges, we carefully treat the oscillating terms which emerge as a result of the chiral decomposition of fermions and do not contribute to the bulk Lagrangian. The obtained result is checked by compared with the exact result derived from the Bethe ansatz, by considering the mode expansion of fermions on the light-cone coordinates. We also give the spin-wave interpretation to the emergence of boundary bound states.