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- Publisher Website: 10.1103/PhysRevB.101.220409
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Article: Automatic differentiation for second renormalization of tensor networks
Title | Automatic differentiation for second renormalization of tensor networks |
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Authors | |
Issue Date | 2020 |
Citation | Physical Review B, 2020, v. 101, n. 22, article no. 220409 How to Cite? |
Abstract | 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 (∂TRG) that can be applied to improve various TRG methods, in an automatic fashion. ∂TRG systematically extends the essential concept of second renormalization [Phys. Rev. Lett. 103, 160601 (2009)PRLTAO0031-900710.1103/PhysRevLett.103.160601] where the tensor environment is computed recursively in the backward iteration. Given the forward TRG process, ∂TRG automatically finds the gradient of local tensors through backpropagation, with which one can deeply "train"the tensor networks. We benchmark ∂TRG in solving the square-lattice Ising model, and we demonstrate its power by simulating one- A nd two-dimensional quantum systems at finite temperature. The global optimization as well as GPU acceleration renders ∂TRG a highly efficient and accurate many-body computation approach. |
Persistent Identifier | http://hdl.handle.net/10722/330668 |
ISSN | 2021 Impact Factor: 3.908 2020 SCImago Journal Rankings: 1.780 |
DC Field | Value | Language |
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dc.contributor.author | Chen, Bin Bin | - |
dc.contributor.author | Gao, Yuan | - |
dc.contributor.author | Guo, Yi Bin | - |
dc.contributor.author | Liu, Yuzhi | - |
dc.contributor.author | Zhao, Hui Hai | - |
dc.contributor.author | Liao, Hai Jun | - |
dc.contributor.author | Wang, Lei | - |
dc.contributor.author | Xiang, Tao | - |
dc.contributor.author | Li, Wei | - |
dc.contributor.author | Xie, Z. Y. | - |
dc.date.accessioned | 2023-09-05T12:12:57Z | - |
dc.date.available | 2023-09-05T12:12:57Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Physical Review B, 2020, v. 101, n. 22, article no. 220409 | - |
dc.identifier.issn | 2469-9950 | - |
dc.identifier.uri | http://hdl.handle.net/10722/330668 | - |
dc.description.abstract | 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 (∂TRG) that can be applied to improve various TRG methods, in an automatic fashion. ∂TRG systematically extends the essential concept of second renormalization [Phys. Rev. Lett. 103, 160601 (2009)PRLTAO0031-900710.1103/PhysRevLett.103.160601] where the tensor environment is computed recursively in the backward iteration. Given the forward TRG process, ∂TRG automatically finds the gradient of local tensors through backpropagation, with which one can deeply "train"the tensor networks. We benchmark ∂TRG in solving the square-lattice Ising model, and we demonstrate its power by simulating one- A nd two-dimensional quantum systems at finite temperature. The global optimization as well as GPU acceleration renders ∂TRG a highly efficient and accurate many-body computation approach. | - |
dc.language | eng | - |
dc.relation.ispartof | Physical Review B | - |
dc.title | Automatic differentiation for second renormalization of tensor networks | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1103/PhysRevB.101.220409 | - |
dc.identifier.scopus | eid_2-s2.0-85092223557 | - |
dc.identifier.volume | 101 | - |
dc.identifier.issue | 22 | - |
dc.identifier.spage | article no. 220409 | - |
dc.identifier.epage | article no. 220409 | - |
dc.identifier.eissn | 2469-9969 | - |