Factorizing F-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective
SG McAteer, M Wheeler
Nuclear Physics B | Elsevier | Published : 2011
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 provide a diagrammatic proof that these F-matrices factorize the tensor Rσ1...n corresponding with elements of the permutation group. We consider in particular the diagram for the tensor Rσc1...n, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators S±i and Szi in terms of the monodromy matrix operators.
We would like to thank Omar Foda for many valuable discussions and for reading the manuscript. S.M. is supported by a Melbourne Research Scholarship. M.W. is supported by a Research Assistantship in the Department of Mathematics and Statistics, University of Melbourne. This work was produced using free, open-source software, in particular the diagrams were created in Inkscape; we would like to acknowledge the thousands of people who have contributed to the development of this software.