  Characterizing out-of-equilibrium many-body dynamics is a complex but crucial
task for quantum applications and the understanding of fundamental phenomena. A
central question is the role of localization in quenching quantum
thermalization, and whether localization survives in the presence of
interactions. The localized phase of interacting systems (many-body
localization, MBL) exhibits a long-time logarithmic growth in entanglement
entropy that distinguishes it from the noninteracting Anderson localization
(AL), but entanglement is difficult to measure experimentally. Here, we present
a novel correlation metric, capable of distinguishing MBL from AL in
high-temperature spin systems. We demonstrate the use of this metric to detect
localization in a natural solidstate spin system using nuclear magnetic
resonance (NMR). We engineer the natural Hamiltonian to controllably introduce
disorder and interactions and observe the emergence of localization. In
particular, while our correlation metric saturates for AL, it keeps increasing
logarithmically for MBL, a behavior reminiscent of entanglement entropy, as we
confirm by simulations. Our results show that our NMR techniques, akin to
measuring out-of-time correlations, are well suited for studying localization
in spin systems.
