  Quantum phase transitions that take place between two distinct topological
phases remain an unexplored area for the applicability of the fidelity
approach. Here, we apply this method to spin systems in two and three
dimensions and show that the fidelity susceptibility can be used to determine
the boundary between different topological phases particular to these models,
while at the same time offering information about the critical exponent of the
correlation length. The success of this approach relies on its independence on
local order parameters or breaking symmetry mechanisms, with which
non-topological phases are usually characterized. We also consider a
topological insulator/superconducting phase transition in three dimensions and
point out the relevant features of fidelity susceptibility at the boundary
between these phases.
