Resumo:

Have you thought about this: every time you tie your shoelaces, you are using a scaling procedure (the tying) to make the topology  (the knot) more obvious? Akin to knot-tying, a renormalization group approach is proposed to identify the topological phase transitions in
topological insulators. The approach further unveils a number of statistical aspects in topological phase transitions, including the correlation function, critical exponents, scaling laws, and universality class. Our result unifies the topological phase transitions in practically all the know topological insulators and topological superconductors (Kitaev, Haldane, Kane-Mele, Majorana chain, Chern insulators, etc) in any dimension and symmetry class, and regardless the transition is driven by noninteracting parameters (chemical potential, magnetic field, film thickness, etc) or interacting parameters (electron-electron interaction, electron-phonon interaction, etc).