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

Response of a quantum disordered spin system to a local periodic drive