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Deep learning topological invariants of band insulators

Author(s)
Sun, Ning; Yi, Jinmin; Zhang, Pengfei; Zhai, Hui; Shen, Huitao
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Abstract
In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90%, even for Hamiltonians whose invariants are beyond the training data set. Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.
Date issued
2018-08
URI
http://hdl.handle.net/1721.1/117272
Department
Massachusetts Institute of Technology. Department of Physics
Journal
Physical Review B
Publisher
American Physical Society
Citation
Sun, Ning, Jinmin Yi, Pengfei Zhang, Huitao Shen and Hui Zhai. "Deep learning topological invariants of band insulators." Physical Review B 98 (2018), 085402.
Version: Final published version
ISSN
2469-9950
2469-9969

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