Machine Learning Topological Invariants with Neural Networks
Name
PhysRevLett.120.066401.pdf
Size
388.67 KB
Format
Adobe PDF
Checksum (MD5)
d9132757fa41523730c6364865e96fc2
Author(s)
Zhang, Pengfei
Shen, Huitao
Zhai, Hui
Date Issued
February 2018
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Zhang, Pengfei et al. "Machine Learning Topological Invariants with Neural Networks." Physical Review Letters 120, 6 (February 2018): 066401 © 2018 American Physical Society
Version
Final published version
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.
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
http://dx.doi.org/10.1103/PhysRevLett.120.066401
