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

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

2002-05-06

arxiv.org/abs/cond-mat/0205101v1

J.Phys.A35:4801-4822,2002

Physics

Condensed Matter

Statistical Mechanics

23 pages and 10 figures

Scientific paper

10.1088/0305-4470/35/23/301

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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