Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

d'Auriac, J. -Ch. Angles; Maillard, J. -M.; Viallet, C. M.

Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

Authors

d'Auriac, J. -Ch. Angles

Maillard, J. -M.

Viallet, C. M.

Description

We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble 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''.
23 pages and 10 figures