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

J. -Ch. Angles d'Auriac·J. -M. Maillard·C. M. Viallet
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Abstract

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''.

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J. -Ch. Angles d'Auriac, J. -M. Maillard, C. M. Viallet. 2002-05-06. Random Matrix Theory and higher genus integrability: the quantum chiral Potts model. https://doi.org/10.1088/0305-4470%2F35%2F23%2F301

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