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.

本文介绍了一种基于神经网络的机器学习方法，可以用于推断不同相的相图，通过获得从个体本征态中提取出来的纠缠谱。该方法在识别 MBL 相转变方面优于传统度量标准（如纠缠熵），从而揭示了更清晰的相边界和关于相图拓扑的新见解，这对于 MBL 相的发现具有参考价值。