Machine learning many-body localization: Search for the elusive nonergodic metal

The many-body localization transition 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 metallic phase associated with a many-body mobility edge exists or not is under active debate. In this Letter, we construct a neural network classifier to investigate the existence of the nonergodic metallic phase in a prototype model using many-body entanglement spectra as the sole diagnostic. We find that such a classifier is able to identify with high confidence the nonergodic metallic phase existing between the many-body localized and the thermal phase. 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 of a novel phase whose existence is unclear.