The persistent homology analysis has been widely used to investigate the phase structure and the spatial structure based on the topological properties of the data space via the filtration of the simplicial complex.
In this talk, I explained how to apply the persistent homology analysis to the QCD effective model with heavy quarks; i.e., the effective Polyakov-line model and the Potts model with the suitably tuned external magnetic field. In this proceedings, the Potts model results are mainly shown.
It is shown that the averaged birth-death time ratio has the same information with the spatial averaged Polyakov-loop and the maximum birth-death time ratio has more information than the averaged birth-death time ratio. Then, the peak structure near the first-order phase transition point and the valley structure before the transition are clarified.
In addition, the plateau behavior is found between the first-order transition and the crossover.