Algorithm

Combinatorics

Machine learning

Quantum entanglement

Physics

Statistical physics

Artificial intelligence

Topology (electrical circuits)

Phase boundary

Topological data analysis

Mathematics

Computer science

Phase (matter)

Artificial neural network

Quantum mechanics

Quantum

Phase diagram

Physical Review Letters

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. Nevertheless, instances of machine learning offering new insights have been rare up to now. 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. To our knowledge this work represents the first example of a machine learning approach revealing new information beyond conventional knowledge.

Machine Learning Out-of-Equilibrium Phases of Matter