  The topological phase transitions in static and periodically driven Kitaev
chains are investigated by means of a renormalization group (RG) approach.
These transitions, across which the numbers of static or Floquet Majorana edge
modes change, are accompanied by divergences of the relevant Berry connections.
These divergences at certain high symmetry points in momentum space form the
basis of the RG approach, through which topological phase boundaries are
identified as a function of system parameters. We also introduce several
aspects to characterize the quantum criticality of the topological phase
transitions in both static and Floquet systems: a correlation function that
measures the overlap of Majorana-Wannier functions, the decay length of the
Majorana edge mode and a scaling law relating the critical exponents. These
indicate a common universal critical behavior for topological phase
transitions, in both static and periodically driven chains. For the latter, the
RG flows additionally display intriguing features related to gap closures at
non-high symmetry points due to momentarily frozen dynamics.
