Universality classes of topological phase transitions
Note: Special time 3:00 on Monday, July 29
In topological insulators and topological superconductors, the change of topological invariant caused by tuning a certain parameter signifies a topological phase transition. Based on the fact that the topological invariant is generally an integration of local curvature in momentum space, we propose a paradigm to characterize the topological phase transitions according to the divergence of the local curvature. The paradigm introduces the notion of correlation function, critical exponents, scaling laws, and renormalization group, applicable to either noninteracting, interacting, or Floquet systems. The notion of universality class and its relation with the symmetry classification will be elaborated. Moreover, we will use machine learning scheme to elaborate that the information about topological phase transitions is entirely encoded in the divergence of the local curvature.