Deep learning topological invariants of band insulators
Name
PhysRevB.98.085402.pdf
Size
1.21 MB
Format
Adobe PDF
Checksum (MD5)
699bf3991dcc839015e12c3ae9ea84f6
Author(s)
Sun, Ning
Yi, Jinmin
Zhang, Pengfei
Zhai, Hui
Shen, Huitao
Date Issued
August 2018
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevB.98.085402
