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

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.

29 pages, plain TEX, UMTG-177

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Cited by in corpus (36)

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• Bulk and Boundary S Matrices for the SU(N) Chain
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• Finite size effects in the XXZ and sine-Gordon models with two boundaries
• The Bethe Ansatz Equations for Reflecting Magnons
• Open Spinning Strings and AdS/dCFT Duality
• Direct Calculation of Breather S Matrices
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain
• Simplified Calculation of Boundary S Matrices
• Kondo impurity at the edge of a superconducting wire
• Integrable O(n) model on the honeycomb lattice via reflection matrices : Surface critical behaviour
• Boundary Quantum Phase Transitions in the Spin $\frac{1}{2}$ Heisenberg Chain with Boundary Magnetic Fields
• Exact solution of the supersymmetric sinh-Gordon model with boundary
• The scaling supersymmetric Yang-Lee model with boundary
• The XXX spin s quantum chain and the alternating $s^1$, $s^2$ chain with boundaries
• Exact Boundary Modes in an Interacting Quantum Wire
• Soliton S matrices for the critical A_{N-1}^(1) chain
• TBA boundary flows in the tricritical Ising field theory
• Edge Modes in One Dimensional Topological Charge Conserving Spin-Triplet Superconductors: Exact Results from Bethe Ansatz
• Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors
• Boundary S-matrix for the Integrable q-Potts Model
• Boundary energy of the open XXX chain with a non-diagonal boundary term
• Boundary S Matrix for the XXZ Chain
• Integrable Four-Fermi Models with a Boundary and Boson-Fermion Duality
• Generic boundary scattering in the open XXZ chain
• Boundary S matrices for the open Hubbard chain with boundary fields
• The sl(N) twisted Yangian: bulk-boundary scattering & defects
• Scattering matrices in the sl(3) twisted Yangian
• Boundary S matrix of an open XXZ spin chain with nondiagonal boundary terms
• Non-diagonal reflection for the non-critical XXZ model
• Exact physical quantities of a competing spin chain in the thermodynamic limit
• Boundary reflection matrices of massive ${\varphi }_{1,3}$-perturbed unitary minimal models
• A note on a boundary sine-Gordon model at the free-Fermion point
• Scattering in Twisted Yangians
• Toda Lattice Models with Boundary