Figure 1

The Yangian and Lie algebra relations of three adjacent particle system in XXZ spin model with periodic boundary condition. This figure shows the transitions between states of the first, second and the last particles’ interaction of N-particle closed XXZ spin chain models. Lie algebra operators \(I_{\alpha }\) represent transitions between states in the same energy level. Yangian operators \(J_{\alpha }\) represent transitions between states in different energy states.