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Original publication:
| Title: | Factorizing $F$-matrices and the XXZ spin-chain: A diagrammatic perspective |
| Author(s): | S.G. McAteer, M. Wheeler |
| As Contributors: | (none claimed) |
| Journal ref.: | Nuclear Physics B 851, 346-379 |
| DOI: | http://dx.doi.org/10.1016/j.nuclphysb.2011.05.019 |
| Date: | 2011-10-11 |
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 $R^σ_{1...n}$ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor $R^{σ_c}_{1...n}$, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators $S^±_i$ and $S^z_i$ in terms of the monodromy matrix operators.