Locality-Induced Hierarchical Backflow Wavefunctions for Correlated Fermions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910276790517760 |
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| author | Zhou, Yu-Tong Zhou, Zheng-Wei Liu, Wen-Yuan |
| author_facet | Zhou, Yu-Tong Zhou, Zheng-Wei Liu, Wen-Yuan |
| contents | We show that locality provides a natural principle to hierarchically organize backflow wavefunctions. This leads us to propose a family of variational fermionic states, termed hierarchical backflow (HB) wavefunctions. The expressive power of HB is systematically improvable, controlled by a path depth $K$ which reflects the range of backflow correlations. At half-filling, the HB with $K=1$ already achieves high energy precision, with an accuracy around $0.5\%$ for system sizes from $4\times 4$ to $10\times 10$. At hole doping $n_h=0.125$, the method scales efficiently to $12\times16$ and $16\times16$ systems, and the energy systematically achieves higher accuracy with $K$ increasing, yielding a clear stripe phase. The HB further enables a local-nonlocal decomposition, naturally bridging to neural quantum states, while featuring compact representations and efficient optimization. Our work reveals locality as a natural organizing principle of backflow wavefunctions, opening a new framework with systematic improvability and interpretability for large-scale simulations of correlated fermion systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locality-Induced Hierarchical Backflow Wavefunctions for Correlated Fermions Zhou, Yu-Tong Zhou, Zheng-Wei Liu, Wen-Yuan Strongly Correlated Electrons Quantum Physics We show that locality provides a natural principle to hierarchically organize backflow wavefunctions. This leads us to propose a family of variational fermionic states, termed hierarchical backflow (HB) wavefunctions. The expressive power of HB is systematically improvable, controlled by a path depth $K$ which reflects the range of backflow correlations. At half-filling, the HB with $K=1$ already achieves high energy precision, with an accuracy around $0.5\%$ for system sizes from $4\times 4$ to $10\times 10$. At hole doping $n_h=0.125$, the method scales efficiently to $12\times16$ and $16\times16$ systems, and the energy systematically achieves higher accuracy with $K$ increasing, yielding a clear stripe phase. The HB further enables a local-nonlocal decomposition, naturally bridging to neural quantum states, while featuring compact representations and efficient optimization. Our work reveals locality as a natural organizing principle of backflow wavefunctions, opening a new framework with systematic improvability and interpretability for large-scale simulations of correlated fermion systems. |
| title | Locality-Induced Hierarchical Backflow Wavefunctions for Correlated Fermions |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2606.00924 |