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arXiv · 1502.04055

Integrability of three dimensional models: cubic equations

Sh. Khachatryan·A. Ferraz·A. Kluemper·A. Sedrakyan
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Abstract

We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.

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Sh. Khachatryan, A. Ferraz, A. Kluemper, A. Sedrakyan. 2015-02-13. Integrability of three dimensional models: cubic equations. https://arxiv.org/abs/1502.04055

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