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...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/117272 https://orcid.org/0000-0003-1667-8011 |
| _version_ | 1811083615633670144 |
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| author | Sun, Ning Yi, Jinmin Zhang, Pengfei Zhai, Hui Shen, Huitao |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Sun, Ning Yi, Jinmin Zhang, Pengfei Zhai, Hui Shen, Huitao |
| author_sort | Sun, Ning |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:35:54Z |
| format | Article |
| id | mit-1721.1/117272 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:35:54Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1172722022-09-28T08:55:56Z Deep learning topological invariants of band insulators Sun, Ning Yi, Jinmin Zhang, Pengfei Zhai, Hui Shen, Huitao Massachusetts Institute of Technology. Department of Physics Shen, Huitao 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. 2018-08-06T12:15:53Z 2018-08-06T12:15:53Z 2018-08 2018-06 2018-08-02T18:00:08Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/117272 Sun, Ning, Jinmin Yi, Pengfei Zhang, Huitao Shen and Hui Zhai. "Deep learning topological invariants of band insulators." Physical Review B 98 (2018), 085402. https://orcid.org/0000-0003-1667-8011 en http://dx.doi.org/10.1103/PhysRevB.98.085402 Physical Review B 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Sun, Ning Yi, Jinmin Zhang, Pengfei Zhai, Hui Shen, Huitao Deep learning topological invariants of band insulators |
| title | Deep learning topological invariants of band insulators |
| title_full | Deep learning topological invariants of band insulators |
| title_fullStr | Deep learning topological invariants of band insulators |
| title_full_unstemmed | Deep learning topological invariants of band insulators |
| title_short | Deep learning topological invariants of band insulators |
| title_sort | deep learning topological invariants of band insulators |
| url | http://hdl.handle.net/1721.1/117272 https://orcid.org/0000-0003-1667-8011 |
| work_keys_str_mv | AT sunning deeplearningtopologicalinvariantsofbandinsulators AT yijinmin deeplearningtopologicalinvariantsofbandinsulators AT zhangpengfei deeplearningtopologicalinvariantsofbandinsulators AT zhaihui deeplearningtopologicalinvariantsofbandinsulators AT shenhuitao deeplearningtopologicalinvariantsofbandinsulators |