Machine learning the many-body localization transition in random spin systems

The transition between thermal and many-body localized phases in isolated random spin systems are typically identified by the distribution of nearest level spacings. In this work, by employing machine learning methodology, we show this transition can be learnt through raw energy spectrum without any pre-processing. After achieving so in conventional random spin chain with differentiable level spacing distributions, we further construct novel models with misleading signatures of level spacing, and show machine can defeat the latter when training data is raw energy spectrum. Our work shows the low-level energy spectrum contains more information than level spacings, and can be captured by machine in a direct while efficient way, which makes it a promising new tool for studying a variety of isolated quantum systems.