Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
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DOI：
10.7566/jpsj.86.044708
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发表时间：
2016-12
影响因子：
1.7
通讯作者：
T. Ohtsuki;T. Ohtsuki
中科院分区：
文献类型：
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作者：
T. Ohtsuki;T. Ohtsuki
三维随机电子系统经历量子相变并显示丰富的相图。相的实例是带隙绝缘体、安德森绝缘体、强和弱拓扑绝缘体、外尔半金属和扩散金属。正如在以前的文件中二维量子相变[J.物理学会。85，123706（2016）]，我们使用基于多层卷积神经网络的图像识别算法来识别特征函数属于哪个相位。研究了局域-离域跃迁的安德森模型、拓扑绝缘体的Wilson-Dirac模型和Weyl半金属的层状Chern绝缘体模型。对于标准传递矩阵法不适用的情况，也可以用这种方法处理。
Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and diffusive metal. As in the previous paper on two-dimensional quantum phase transitions [J. Phys. Soc. Jpn. 85, 123706 (2016)], we use an image recognition algorithm based on a multilayered convolutional neural network to identify which phase the eigenfunction belongs to. The Anderson model for localization–delocalization transition, the Wilson–Dirac model for topological insulators, and the layered Chern insulator model for Weyl semimetal are studied. The situation where the standard transfer matrix approach is not applicable is also treated by this method.