تقرير
Haldane Bundles: A Dataset for Learning to Predict the Chern Number of Line Bundles on the Torus
| العنوان: | Haldane Bundles: A Dataset for Learning to Predict the Chern Number of Line Bundles on the Torus |
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| المؤلفون: | Tipton, Cody, Coda, Elizabeth, Brown, Davis, Bittner, Alyson, Lee, Jung, Jorgenson, Grayson, Emerson, Tegan, Kvinge, Henry |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Mesoscale and Nanoscale Physics, Computer Science - Machine Learning, Mathematics - Algebraic Topology |
| الوصف: | Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {\emph{Haldane bundle dataset}}, which consists of synthetically generated complex line bundles on the $2$-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.04600 |
| رقم الأكسشن: | edsarx.2312.04600 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |