  We introduce the operator fidelity and propose to use its susceptibility for
characterizing the sensitivity of quantum systems to perturbations. Two typical
models are addressed: one is the transverse Ising model exhibiting a quantum
phase transition, and the other is the one dimensional Heisenberg spin chain
with next-nearest-neighbor interactions, which has the degeneracy. It is
revealed that the operator fidelity susceptibility is a good indicator of
quantum criticality regardless of the system degeneracy.
