Random matrix theory and higher genus integrability: the quantum chiral Potts model

We perform a random matrix theory (RMT) analysis of the quantum fourstate chiral Potts chain for different sizes of the chain up to size L = 8. Ou ra nalysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ‘higher genus integrability’.