GAUSSIAN ORTHOGONAL ENSEMBLE FOR THE LEVEL SPACING STATISTICS OF THE QUANTUM FOUR-STATE CHIRAL POTTS MODEL

We have performed a Random Matrix Theory (RMT) analysis of the quantum four state chiral Potts chain for different sizes of the quantum chain up to eight sites, and for different unfolding methods. Our analysis shows that one generically has a Gaussian Orthogonal Ensemble statistics for the unfolded spectrum instead of the GUE statistics one could expect. Furthermore a change from the generic GOE distribution to a Poisson distribution occurs when the hamiltonian becomes integrable. Therefore, the RMT analysis can be seen as a detector of "higher genus integrability".