Machine learning out-of-equilibrium phases of matter

TL;DR

This paper demonstrates that neural networks can effectively identify and delineate many-body localized and thermal phases using entanglement spectra, outperforming traditional metrics and enabling rapid exploration of phase diagrams.

Contribution

It introduces a novel simplicial geometry method for extracting phase boundaries and shows that a single neural network can reveal new insights into MBL phases beyond conventional methods.

Findings

Neural network accurately decodes MBL and thermal phases from entanglement spectra.

The simplicial geometry method outperforms entanglement entropy in identifying phase transitions.

Machine learning enables rapid exploration of phase space and discovery of new MBL phases.

Abstract

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.