Machine Learning Topological Invariants with Neural Networks

Physical Review Letters
Pengfei ZhangHui Zhai

Abstract

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.

References

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Citations

Jul 24, 2018·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Qing-Qing ChengYi-Fei Wang
Jul 25, 2019·Physical Review. E·Julian ZimmermannDaniela Rupp
Sep 27, 2018·Physical Review. E·Dongkyu Kim, Dong-Hee Kim
Apr 20, 2019·Physical Review. E·Wanzhou ZhangTzu-Chieh Wei
May 22, 2019·Physical Review. E·Xin XuYing Jiang
Jun 6, 2020·Physical Review Letters·Huitao ShenHui Zhai
Jul 10, 2019·Physical Review Letters·Wenqian LianLuming Duan
Mar 24, 2020·Physical Review Letters·Tom VieijraFrank Verstraete
Jun 23, 2020·Physical Review Letters·Mathias S Scheurer, Robert-Jan Slager
May 23, 2020·Physical Review Letters·Yang LongHong Chen
Sep 10, 2019·Nanoscale·Zhao HuangJianfeng Zang
Apr 4, 2020·Physical Review Letters·Xiwang LiuWeifeng Yang
Jul 25, 2020·Light, Science & Applications·Minkyung KimJunsuk Rho
Sep 30, 2020·Optics Express·Robin SinghBrian W Anthony
Oct 6, 2020·Physical Review Letters·Eran LustigMordechai Segev
Oct 24, 2019·Physical Review. E·William Gilpin
Sep 16, 2020·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Edwin BedollaRamón Castañeda-Priego
Jun 18, 2021·Physical Review. E·Quoc Hoan TranYoshihiko Hasegawa
Jul 3, 2021·Physical Review Letters·Li-Wei Yu, Dong-Ling Deng
Jul 21, 2021·Light, Science & Applications·Minkyung KimJunsuk Rho
Sep 3, 2019·Journal of Chemical Theory and Computation·Cesar A LöpezBoian S Alexandrov
Aug 27, 2021·Journal of Chemical Information and Modeling·Liyuan Huang, Chen Ling

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