Integrable spin systems with long-range interactions
A method to construct spin Hamiltonians from the \(R\)-matrix is presented. These Hamiltonians describe quantum spin chains where all spins interact through long-range pairwise interactions. The Yang-Baxter relation is considered as a sufficient condition of integrability and then it is proven that the inhomogeneous \(R\)-matrices give integrable spin chains with long-range interactions. The explicit relation between the Hamiltonian and the \(R\)-matrix is obtained and then some applications to various models including spin-1/2 and spin-1 cases are presented. Based on the method previous developed, the integrability of the Haldane-Shastry model and its extension is discussed.
scientific article; zbMATH DE number 86304