Using notation inherited from the six-vertex model, we construct diagrams that represent the action of the factorizing $F$-matrices associated to the finite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorize the tensor $R^{ \sigma}_{ 1... n}$ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor $R^{ \sigma_c}_{ 1... n}$, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators $S_i^{ \pm}$ and $S_i^{ z}$ in terms of the monodromy matrix operators.
Categories: math-ph hep-th math.MP