sl(2|1)(2) Gaudin magnet and its associated Knizhnik–Zamolodchikov equation

2004/06/14 by V. Kurak, A. Lima-Santos · 11 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic number #Algebraic structures and combinatorial models #Bethe ansatz #Chemistry #Coulomb #Eigenvalues and eigenvectors #Integrable system #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Nonlinear Waves and Solitons #Physics #Quantum #Quantum mechanics #Semiclassical physics #Trigonometry #hep-th #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2004.09.022

published in Nuclear Physics B 701(3), 497-515 (Elsevier BV) · 20 pages, LaTex

arxiv created 2004/06/14 · openalex publication_date 2004/10/05 · openalex created_date 2020/05/13 · openalex updated_date 2026/08/05

Abstract

The semiclassical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models for the sl(2|1)⁽²⁾ R-matrix. We find the spectra and eigenvectors of the N-1 independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.

Citations

• Quantum Inverse Scattering Method and Correlation Functions
• Current algebra and Wess-Zumino model in two dimensions
• Diagonalisation d'une classe d'hamiltoniens de spin
• Bethe ansätze for 19-vertex models
• KNIZHNIK–ZAMOLODCHIKOV–BERNARD EQUATIONS CONNECTED WITH THE EIGHT-VERTEX MODEL

Cited by

• Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model