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

TL;DR

This paper uses Random Matrix Theory to analyze the quantum chiral Potts model, revealing a transition from GOE to Poisson statistics that indicates integrability and higher genus algebraic structures.

Contribution

It demonstrates that RMT can detect higher genus integrability in the quantum chiral Potts model, linking spectral statistics to algebraic properties.

Findings

GOE statistics suggest generalized time-reversal invariance

Transition to Poisson distribution at integrability points

RMT analysis detects higher genus integrability

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''.