Factorizing F -matrices and the XXZ spin-12 chain: A diagrammatic perspective

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-12 chain. We provide a diagrammatic proof that these F  -matrices factorize the tensor R1…nσ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor R1…nσc, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators Si± and Siz in terms of the monodromy matrix operators.