Solutions of the reflection equation for the vertex model

2006/08/27 by A. Lima-Santos, M. J. Martins, M.J. Martins
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #hep-th #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2006.09.023

published as Nucl.Phys.B760:184-196,2007 · 18 pages

arxiv created 2006/08/27 · openalex publication_date 2006/10/19 · arxiv updated 2010/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental U_q[G₂] vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half are non-diagonal. The latter are parameterized by two continuous parameters but only one solution has all entries non-null. The non-diagonal solutions do not reduce to diagonal ones at any special limit of the free-parameters.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• Integrable XYZ Spin Chain with Boundaries
• Boundary Yang-Baxter equation in the RSOS/SOS representation
• Row transfer matrix functional relations for Baxter's eight-vertex and six-vertex models with open boundaries via more general reflection matrices
• Boundary conditions for integrable quantum systems
• Dn+1(2) reflection K-matrices