Random Matrix Theory and higher genus integrability: the quantum chiral Potts model
Statistical Mechanics
2008-11-26 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
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''.
Cite
@article{arxiv.cond-mat/0205101,
title = {Random Matrix Theory and higher genus integrability: the quantum chiral Potts model},
author = {J. -Ch. Angles d'Auriac and J. -M. Maillard and C. M. Viallet},
journal= {arXiv preprint arXiv:cond-mat/0205101},
year = {2008}
}
Comments
23 pages and 10 figures