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

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 $R_{\mathrm{1...}n}^{\sigma }$ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor $R_{\mathrm{1...}n}^{{\sigma }_c}$, 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.

arXiv comment26 pages, extra references added, typographical errors corrected

References in corpus (5)

• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• On the quantum inverse scattering problem
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• Solution of the quantum inverse problem

Cited by in corpus (4)

• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Bethe Ansatz, Quantum Circuits, and the F-basis
• The factorized F-matrices for arbitrary U(1)^(N-1) integrable vertex models
• On factorizing $F$-matrices in $Y(s{l}_n)$ and $U_q(\widehat{s{l}_n})$ spin chains