تقرير
Automatic Differentiation for Second Renormalization of Tensor Networks
| العنوان: | Automatic Differentiation for Second Renormalization of Tensor Networks |
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| المؤلفون: | Chen, Bin-Bin, Gao, Yuan, Guo, Yi-Bin, Liu, Yuzhi, Zhao, Hui-Hai, Liao, Hai-Jun, Wang, Lei, Xiang, Tao, Li, Wei, Xie, Z. Y. |
| المصدر: | Phys. Rev. B 101, 220409 (2020) |
| سنة النشر: | 2019 |
| المجموعة: | Condensed Matter Physics (Other) |
| مصطلحات موضوعية: | Condensed Matter - Strongly Correlated Electrons, Physics - Computational Physics |
| الوصف: | Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a uniform framework of differentiable TRG ($\partial$TRG) that can be applied to improve various TRG methods, in an automatic fashion. Essentially, $\partial$TRG systematically extends the concept of second renormalization [PRL 103, 160601 (2009)] where the tensor environment is computed recursively in the backward iteration, in the sense that given the forward process of TRG, $\partial$TRG automatically finds the gradient through backpropagation, with which one can deeply "train" the tensor networks. We benchmark $\partial$TRG in solving the square-lattice Ising model, and demonstrate its power by simulating one- and two-dimensional quantum systems at finite temperature. The deep optimization as well as GPU acceleration renders $\partial$TRG manybody simulations with high efficiency and accuracy. Comment: 13 pages, 9 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevB.101.220409 |
| URL الوصول: | http://arxiv.org/abs/1912.02780 |
| رقم الأكسشن: | edsarx.1912.02780 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevB.101.220409 |
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