Figure 2

shows the generalization of the interaction model of any three adjacent particles of the closed XXZ spin chain model. In the action of three particles, the heavy solid line means that the action of two adjacent particles is additive, and the dotted line means that the action of two adjacent particles is subtractive. Figure 2 contains all the generalizations of closed XXZ spin chain.e The generalization rules: the double arrow indicates that the operator \(\uparrow , \downarrow \) are added in the penultimate position to generalize, the dotted arrow indicates that the operators are added at the final position, the single arrow indicates that the operators are added at the foremost position, the dotted arrow indicates that the operators are added at the second positive.