30 May 2011
Factorizing \(F\)-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective (paper)
S.G. Mc Ateer and M. Wheeler
Abstract: 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.
(Nuclear Physics B, also available from arXiv:1103.4488 [math-ph].)