2007/03/10 by P. N. Bibikov, Bibikov, P. N.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.nlin/0703017
openalex publication_date 2007/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several complete systems of integrability conditions on a spin chain Hamiltonian density matrix are presented. The corresponding formulas for R-matrices are also given. The latter is expressed via the local Hamiltonian density in the form similar to spin one half XXX and XXZ models. The result is applied to the problem of integrability of SU(2)× SU(2)- and SU(2)× U(1)-invariant spin-orbital chains (the Kugel-Homskii-Inagaki model). The eight new integrable cases are found. One of them corresponds to the Temperley-Lieb algebra, the others three to the algebra associated with the XXX, XXZ and graded XXZ models. The last two R-matrices are also presented.