Department of Physics, Cornell University, Ithaca, New York 14853, USA.
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev Lett. 2018 Jun 22;120(25):257204. doi: 10.1103/PhysRevLett.120.257204.
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 (MBL) 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 multipartite phase boundaries. We find that this method outperforms conventional metrics for identifying MBL phase transitions, revealing a sharper phase boundary and shedding new insight on 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 Letter represents the first example of a standard machine learning approach revealing new information on phase transitions.
基于神经网络的机器学习正在成为获取相图的有力工具，特别是在传统的使用局部平衡序参数的回归方案不可用时，例如在多体局域（MBL）或拓扑相中。然而，到目前为止，提供新见解的机器学习实例仍然很少。在这里，我们展示了单个前馈神经网络可以使用从单个本征态获得的纠缠谱来解码两个不同的 MBL 相和热化相的定义结构。为此，我们引入了一种基于单纯形几何的方法来提取多部分相界。我们发现，这种方法比传统的用于识别 MBL 相变的度量标准表现更好，揭示了更尖锐的相界，并为相图的拓扑结构提供了新的见解。此外，我们从单个无序配置中获得的相图证实了我们在这里建立的基于机器学习的方法可以快速探索能够辅助发现新 MBL 相的大相空间。据我们所知，这封信件代表了标准机器学习方法揭示相变新信息的第一个示例。
