Journal
ANNALS OF PHYSICS
Volume 435, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2021.168500
Keywords
Anderson transition; Quantum phase transition; Quantum kicked rotor; Machine learning; Convolutional neural network; Long short-term memory network
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Funding
- Japan Society for Promotion of Science (JSPS) KAKENHI [16H06345, 19H00658]
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This study utilizes CNN and LSTM to analyze quantum phases in random electron systems, obtaining phase diagrams for Anderson transitions, quantum percolations, and disordered topological systems.
Using the multilayer convolutional neural network (CNN), we can detect the quantum phases in random electron systems, and phase diagrams of two and higher dimensional Anderson transitions and quantum percolations as well as disordered topological systems have been obtained. Here, instead of using CNN to analyze the wave functions, we analyze the dynamics of wave packets via long short-term memory network (LSTM). We adopt the quasi-periodic quantum kicked rotors, which simulate the three and four dimensional Anderson transitions. By supervised training, we let LSTM extract the features of the time series of wave packet displacements in localized and delocalized phases. We then simulate the wave packets in unknown phases and let LSTM classify the time series to localized and delocalized phases. We compare the phase diagrams obtained by LSTM and those obtained by CNN. (C) 2021 Elsevier Inc. All rights reserved.
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