Algebraic Bethe ansatz for 19-vertex models with upper triangularK-matrices

2014/06/30 by Rodrigo A. Pimenta, R. A. Pimenta, A. Lima-Santos
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Combinatorics #Computer science #Diagonal #Eigenvalues and eigenvectors #Geometry #Graph #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Transfer matrix #Triangular matrix #Vertex (graph theory) #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/1742-5468/2014/11/p11007

published as J. Stat. Mech. (2014) P11007 · 30 pages; v2: typos corrected, published

arxiv created 2014/11/06 · openalex publication_date 2014/11/06 · arxiv updated 2014/11/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

By means of an algebraic Bethe ansatz approach, we study the Zamolodchikov–Fateev and Izergin–Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors are used to diagonalize the associated transfer matrix. The eigenvalues as well as the Bethe equations are presented.

Citations

• Boundary K-matrix for the quantum Mikhailov-Shabat model
• The inverse scattering method approach to the quantum Shabat-Mikhailov model
• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Quantum inverse problem method. I
• Reflection K-matrices of the 19-vertex model and XXZ spin-1 chain with general boundary terms
• Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries
• Boundary conditions for integrable quantum systems