  The breaking of ergodicity in isolated quantum systems with a single-particle
mobility edge is an intriguing subject that has not yet been fully understood.
In particular, whether a nonergodic but metallic phase exists or not in the
presence of a one-dimensional quasiperiodic potential is currently under active
debate. In this Letter, we develop a neural-network-based approach to
investigate the existence of this nonergodic metallic phase in a prototype
model using many-body entanglement spectra as the sole diagnostic. We find that
such a method identifies with high confidence the existence of a nonergodic
metallic phase in the midspectrum at an intermediate quasiperiodic potential
strength. Our neural-network based approach shows how supervised machine
learning can be applied not only in locating phase boundaries but also in
providing a way to definitively examine the existence or not of a novel phase.
