  We analyze ground-state behaviors of fidelity susceptibility (FS) and show
that the FS has its own distinct dimension instead of real system's dimension
in general quantum phases. The scaling relation of the FS in quantum phase
transitions (QPTs) is then established on more general grounds. Depending on
whether the FS's dimensions of two neighboring quantum phases are the same or
not, we are able to classify QPTs into two distinct types. For the latter type,
the change in the FS's dimension is a characteristic that separates two phases.
As a non-trivial application to the Kitaev honeycomb model, we find that the FS
is proportional to $L^2\ln L$ in the gapless phase, while $L^2$ in the gapped
phase. Therefore, the extra dimension of $\ln L$ can be used as a
characteristic of the gapless phase.
