  We study slightly generalized quantum fidelity susceptibilities where the
differential change in the fidelity is measured with respect to a different
term than the one used for driving the system towards a quantum phase
transition. As a model system we use the spin-1/2 J1-J2 antiferromagnetic
Heisenberg chain. For this model, we study three fidelity susceptibilities,
chi_p, chi_D and chi_AF, which are related to the spin stiffness, the dimer
order and antiferromagnetic order, respectively. All these ground-state
fidelity susceptibilities are sensitive to the phase diagram of the J1-J2
model. We show that they all can accurately identify a quantum critical point
in this model occurring at J2 = 0.241J1 between a gapless Heisenberg phase for
J2 < J2_critical and a dimerized phase for J2 > J2_critical. This phase
transition, in the Berezinskii-Kosterlitz-Thouless universality class, is
controlled by a marginal operator and is therefore particularly difficult to
observe.
