Analysis of the deconfinement transition using persistent homology

In low temperature region, quarks are confined in hadrons, while they behave like free particles in high temperature. This is called deconfinement phase transition. In quenched QCD, Polyakov loop is the order parameter of the deconfinement phase transition. However, considering QCD with dynamical quarks, we cannot define this as a strictly order parameter. Then, we applied analysis based on "persistent homology" to Polyakov loop and investigated deconfinement phase transition in the effective Polyakov-line model.