Chiral Potts model and the discrete Sine-Gordon model at roots of unity

Understand

The discrete quantum Sine-Gordon model at roots of unity remarkably combines a classical integrable system with an integrable quantum spin system, whose parameters obey classical equations of motion.

• We show that the fundamental R-matrix of the model (which satisfies a difference property Yang-Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part.
• The classical part of the $R$-matrix itself satisfies the quantum Yang-Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part.
• We show that the resulting equation exactly coincides with the star-triangle relation of the N-state chiral Potts model.