  We propose to apply spin noise spectroscopy (SNS) to detect many-body
localization (MBL) in disordered spin systems. The SNS methods are relatively
non-invasive technique to probe spontaneous spin fluctuations. We here show
that the spin noise signals obtained by cross-correlation SNS with two probe
beams can be used to separate the MBL phase from a noninteracting Anderson
localized phase and a delocalized (diffusive) phase in the studied models for
which we numerically calculate real time spin noise signals and their power
spectra. For the archetypical case of the disordered XXZ spin chain we also
develop a simple phenomenological model.
