Geodesic
Solutions of the~Yang--Baxter equation associated with a~topological
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 19-38

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We discuss a new type of solutions of the Yang–Baxter equation, called type-II solutions. They are related to quantum entanglements. The action of the corresponding braiding operator on the topological basis associated with a topological quantum field theory generates a $(2J{+}1)$-dimensional matrix form of the $R$-matrix for spin $J$, i.e., the Wigner function $D$ with the spectral parameter $\theta$ denoting the entanglement degree. We present concrete examples for $J=1/2$ and $J=1$ in an explicit form. We show that the Hamiltonian related to the type-II $R$-matrix is Kitaev's toy model.
Keywords: Yang–Baxter equation, topological quantum field theory, Wigner function $D$, Kitaev's toy model.
Mots-clés : quantum entanglement 
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     author = {Mo-Lin Ge and Li-Wei Yu and Kang Xue and Qing Zhao},
     title = {Solutions of {the~Yang--Baxter} equation associated with a~topological},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     number = {1},
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Mo-Lin Ge; Li-Wei Yu; Kang Xue; Qing Zhao. Solutions of the~Yang--Baxter equation associated with a~topological. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 1, pp. 19-38. http://geodesic.mathdoc.fr/item/TMF_2014_181_1_a1/