  We consider a one-dimensional spin chain system with quenched disorder and in
the presence of a local periodic drive. We study the time evolution of the
system in the Floquet basis and evaluate the fidelity susceptibility, which is
a measure of how a given state changes under a small perturbation, of states to
a weak periodic drive. We demonstrate that the statistical properties of the
fidelity susceptibility over different disorder realizations can be used to
identify two phases of the system: (1) the many-body localized phase, in which
the susceptibility exhibits long tails while its average value decreases
rapidly as disorder increases; and (2) the ergodic phase, in which the
susceptibility distribution is narrow and its average value weakly depends on
disorder. This distinction in the average value of the susceptibility between
the two phases develops readily for systems with ten or more spins. Therefore,
recently built networks of qubits subject to a local drive can simulate
dynamics of a system in the many-body localization regime. We also show that
the spin accumulation speed is correlated with the fidelity susceptibility and
can also be used to distinguish the two phases.
