Learning single-particle mobility edges by a neural network based on data compression

The breaking of the well-known Aubry-Andr\'e model with a single-particle mobility edge (SPME) is a intriguing subject that has not yet been fully understood. In particular, how to accurately and efficiently recognize a SPME in an optical lattice is currently under active debate. In this work, we develop a data compression-based neural network (DCNN) approach to identify SPMEs in one-dimensional quasiperiodic optical lattice using eigenstates as the sole diagnostic. We find that such method can successfully identify SPMEs of a large system only using a small network trained by the small system data, without onerously and repetitively training a new and large-scale network by massive data of a large system. Furthermore, we show that this method is also applicable to recognize more complex phase transitions, such as many-body localization. Our DCNN approach first paves the way for the development of a generic tool for identifying unexplored phase transitions in large systems.