Machine learning out-of-equilibrium phases of matter

Neural network based machine learning is emerging as a powerful tool for obtaining phase diagrams when traditional regression schemes using local equilibrium order parameters are not available, as in many-body localized or topological phases. Here we show that a single feed-forward neural network can decode the defining structures of two distinct MBL phases and a thermalizing phase, using entanglement spectra obtained from individual eigenstates. For this, we introduce a simplicial geometry based method for extracting multi-partite phase boundaries. We find that this method outperforms conventional metrics (like the entanglement entropy) for identifying MBL phase transitions, revealing a sharper phase boundary and shedding new insight into the topology of the phase diagram. Furthermore, the phase diagram we acquire from a single disorder configuration confirms that the machine-learning based approach we establish here can enable speedy exploration of large phase spaces that can assist with the discovery of new MBL phases.