Factorizing $F$-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective

Details Factorizing $F$-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective Factorizing $F$-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective

2011-03-23

arxiv.org/abs/1103.4488v2

Nucl.Phys.B851:346-379,2011

Physics

Mathematical Physics

26 pages, extra references added, typographical errors corrected

Scientific paper

10.1016/j.nuclphysb.2011.05.019

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.

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