We consider the su(p) spin chains with long-range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities of the dynamical models and we diagonalise them. In the spin chain case, we establish the connection between the degeneracies of the spectrum and the representation theory of the Yangians. We use a correspondence with the dynamical models to diagonalise the Hamiltonian. Finally, we extend the previous results to the case of a trigonometric R-matrix.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics