  We analyze a disordered central spin model, where a central spin interacts
equally with each spin in a periodic one dimensional random-field Heisenberg
chain. If the Heisenberg chain is initially in the many-body localized (MBL)
phase, we find that the coupling to the central spin suffices to delocalize the
chain for a substantial range of coupling strengths. We calculate the phase
diagram of the model and identify the phase boundary between the MBL and
ergodic phase. Within the localized phase, the central spin significantly
enhances the rate of the logarithmic entanglement growth and its saturation
value. We attribute the increase in entanglement entropy to a non-extensive
enhancement of magnetization fluctuations induced by the central spin. Finally,
we demonstrate that correlation functions of the central spin can be utilized
to distinguish between MBL and ergodic phases of the 1D chain. Hence, we
propose the use of a central spin as a possible experimental probe to identify
the MBL phase.

Disordered Systems and Neural Networks;Quantum Physics