Application of deep learning to the quantum phase transition in random electron systems

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K18763
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Research Field: Condensed matter physics and related fields
• Research Institution: Sophia University
• Principal Investigator: Ohtsuki Tomi 上智大学, 理工学部, 教授 (50201976)
• Project Period (FY): 2017-06-30 – 2020-03-31
• Keywords: 深層学習 / 機械学習 / 量子相転移 / トポロジカル系 / アンダーソン転移 / 量子パーコレーション

Outline of Final Research Achievements

Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. One of the applications is analyzing the wave functions and determining their quantum phases. We have used the multilayer convolutional neural network, so-called deep learning, to determine the quantum phases in random electron systems. After training the neural network by the supervised learning of wave functions in restricted parameter regions in known phases, the neural networks can determine the phases of the wave functions in wide parameter regions in unknown phases; hence, the phase diagrams are obtained. We demonstrate the validity and generality of this method by drawing the phase diagrams of two- and higher dimensional Anderson metal-insulator transitions and quantum percolations as well as disordered topological systems. Both real-space and Fourier space wave functions are analyzed. The advantages and disadvantages over conventional methods are discussed.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

機械学習，広くは人工知能の手法が，金属や半導体，絶縁体の性質を調べる固体物理においても有効性であることを示した。動物や人の画像認識として一般に親しまれている深層学習が，固体物理学に応用できることを示し，この手法の有効性を明らかにできた。