Integrability of three dimensional models: cubic equations

2015/02/13 by Khachatryan, Sh., Ferraz, A., Kluemper, A. +1
#FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1502.04055

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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