Classification of reflection matrices related to (super-)Yangians and application to open spin chain models

2003/04/30 by D. Arnaudon, Jean Avan, J. Avan +6 · 37 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Chain (unit) #Computer science #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Reflection (computer programming) #hep-th #math-ph #math.MP #math.QA #msc:17B37 #msc:81R50

paper · pdf · doi:10.1016/s0550-3213(03)00503-0

published in Nuclear Physics B 668(3), 469-505 (Elsevier BV) · 36 pages ; references added ; typos corrected, precisions added

openalex publication_date 2003/08/01 · arxiv created 2003/10/02 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe Ansatz resolution for the so(m) and sp(n) open spin chains with boundary conditions described by the diagonal solutions.

Citations

• Boundary K-matrix for the quantum Mikhailov-Shabat model
• Analytical Bethe ansatz for a A2n-1(2), Bn(1), Cn(1), Dn(1)quantum-algebra-invariant open spin chains
• New non-diagonal solutions to the a_n⁽¹⁾ boundary Yang-Baxter equation
• Row transfer matrix functional relations for Baxter's eight-vertex and six-vertex models with open boundaries via more general reflection matrices
• Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom
• Direct calculation of the S matrix in the massive thirring model
• Boundary conditions for integrable quantum systems
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Cited by

• Bethe ansatz equations and exact S matrices for the osp(M|2n) open super-spin chain