Probing many-body localization by spin noise spectroscopy

We propose to apply spin noise spectroscopy (SNS) to detect many-body localization (MBL) in disordered spin systems. The SNS methods are relatively noninvasive techniques to probe spontaneous spin fluctuations. Here, we 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 an archetypical case of the disordered XXZ spin chain, we also develop a simple phenomenological model.