  The notion of fidelity susceptibility, introduced within the context of
quantum metric tensor, has been an important quantity to characterize the
criticality near quantum phase transitions. We demonstrate that for topological
phase transitions in Dirac models, provided the momentum space is treated as
the manifold of the quantum metric, the fidelity susceptibility coincides with
the curvature function whose integration gives the topological invariant. Thus
the quantum criticality of the curvature function near a topological phase
transition also describes the criticality of the fidelity susceptibility, and
the correlation length extracted from the curvature function also gives a
momentum scale over which the fidelity susceptibility decays. To map out the
profile and criticality of the fidelity susceptibility, we turn to quantum
walks that simulate one-dimensional class BDI and two-dimensional class D Dirac
models, and demonstrate their accuracy in capturing the critical exponents and
scaling laws near topological phase transitions.
