Some Aspects of Persistent Homology Analysis on Phase Transition: Examples in an Effective QCD Model with Heavy Quarks

Abstract

Recently, persistent homology analysis has been used to investigate phase structure. In this study, we apply persistent homology analysis to the QCD effective model with heavy quarks at finite imaginary chemical potential; i.e., the Potts model with the suitably tuned external field. Since we try to obtain a deeper understanding of the relationship between persistent homology and phase transition in QCD, we consider the imaginary chemical potential because the clear phase transition, which is closely related to the confinement-deconfinement transition, exists. In the actual analysis, we employ the point-cloud approach to consider persistent homology. In addition, we investigate the fluctuation of persistent diagrams to obtain additional information on the relationship between the spatial topology and the phase transition.