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

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''.

arXiv comment23 pages and 10 figures

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• Inozemtsev's hyperbolic spin model and its related spin chain
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• $1/f^{\alpha }$ noise and integrable systems
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators