Interpretable order parameters for lattice field theories from topological data analysis
Daniel Spitz (MPI Leipzig)

Finding interpretable order parameters for the detection of topological dynamics and critical phenomena can be a challenging endeavour in lattice field theories. Tailored to detect and quantify topological structures in noisy data, topological data analysis (TDA) allows for the construction of sensitive observables. In this talk I will discuss two research projects, which highlight the potential of TDA for lattice field-theoretical studies. The first utilizes TDA to investigate the role of topological defects in regimes governed by universal self-similar dynamics. More specifically, in simulations of the paradigmatic O(N) vector model, the dynamics of topological defects can be studied via Betti curves computed from local energy densities. Based on Monte Carlo simulations of SU(2) lattice gauge theory, the second project shows how TDA computed from chromoelectric and -magnetic fields, topological densities and Polyakov loops can be used to uncover a multifaceted picture of the deconfinement phase transition.

This application-oriented talk is based on joint work with Viktoria Noel, Jan Pawlowski and Julian Urban.