Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916273514872832 |
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| author | Zhou, Yu-Tong Zhou, Zheng-Wei Liang, Xiao |
| author_facet | Zhou, Yu-Tong Zhou, Zheng-Wei Liang, Xiao |
| contents | The quantum many-body problem is an important topic in condensed matter physics. To efficiently solve the problem, several methods have been developped to improve the representation ability of wave-functions.
For the Fermi-Hubbard model under periodic boundary conditions, current state-of-the-art methods are neural network backflows and the hidden fermion Slater determinant.
The backflow correction is an efficient way to improve the Slater determinant of free-particles.
In this work we propose a tensor representation of the backflow corrected wave-function, we show that for the spinless $t$-$V$ model, the energy precision is competitive or even lower than current state-of-the-art fermionic tensor network methods.
For models with spin, we further improve the representation ability by considering backflows on fictitious particles with different spins, thus naturally introducing non-zero backflow corrections when the orbital and the particle have opposite spins.
We benchmark our method on molecules under STO-3G basis and the Fermi-Hubbard model with periodic and cylindrical boudary conditions.
We show that the tensor representation of backflow corrections achieves competitive or even lower energy results than current state-of-the-art neural network methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections Zhou, Yu-Tong Zhou, Zheng-Wei Liang, Xiao Strongly Correlated Electrons Quantum Gases Quantum Physics The quantum many-body problem is an important topic in condensed matter physics. To efficiently solve the problem, several methods have been developped to improve the representation ability of wave-functions. For the Fermi-Hubbard model under periodic boundary conditions, current state-of-the-art methods are neural network backflows and the hidden fermion Slater determinant. The backflow correction is an efficient way to improve the Slater determinant of free-particles. In this work we propose a tensor representation of the backflow corrected wave-function, we show that for the spinless $t$-$V$ model, the energy precision is competitive or even lower than current state-of-the-art fermionic tensor network methods. For models with spin, we further improve the representation ability by considering backflows on fictitious particles with different spins, thus naturally introducing non-zero backflow corrections when the orbital and the particle have opposite spins. We benchmark our method on molecules under STO-3G basis and the Fermi-Hubbard model with periodic and cylindrical boudary conditions. We show that the tensor representation of backflow corrections achieves competitive or even lower energy results than current state-of-the-art neural network methods. |
| title | Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections |
| topic | Strongly Correlated Electrons Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2308.11823 |