  We study non-local measures of spectral correlations and their utility in
characterizing and distinguishing between the distinct eigenstate phases of
quantum chaotic and many-body localized systems. We focus on two related
quantities, the spectral form factor and the density of all spectral gaps, and
show that they furnish unique signatures that can be used to sharply identify
the two phases. We demonstrate this by numerically studying three
one-dimensional quantum spin chain models with (i) quenched disorder, (ii)
periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in
what ways the signatures are universal and in what ways they are not. More
generally, this thorough analysis is expected to play a useful role in
classifying phases of disorder systems.
