Deep learning topological invariants of band insulators

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...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. B 2018-08, Vol.98 (8), p.085402, Article 085402
Main Authors: Sun, Ning, Yi, Jinmin, Zhang, Pengfei, Shen, Huitao, Zhai, Hui
Format: Article
Language:English
Subjects:
Artificial neural networks
Curvature
Deep learning
Insulators
Invariants
Mathematical models
Neural networks
Winding
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.98.085402