A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one)
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917008635854848 |
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| author | Fu, Liang |
| author_facet | Fu, Liang |
| contents | Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space. Building on this lifting, we obtain a \emph{parity-graded representation} of fermionic wavefunctions, expressed in terms of symmetric feature variables that encode particle configuration and antisymmetric feature variables that encode exchange statistics. This representation is both exact and minimal: the number of required features scales as $D\sim N^d$ ($d$ is spatial dimension) or $D\sim N$ depending on the symmetric feature maps employed. Our results provide a rigorous mathematical foundation for efficient representations of fermionic wavefunctions and enable scalable and systematically improvable neural network solvers for many-electron systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_11431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one) Fu, Liang Strongly Correlated Electrons Mathematical Physics Quantum Physics Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them to continuous symmetric functions defined on an enlarged space. Building on this lifting, we obtain a \emph{parity-graded representation} of fermionic wavefunctions, expressed in terms of symmetric feature variables that encode particle configuration and antisymmetric feature variables that encode exchange statistics. This representation is both exact and minimal: the number of required features scales as $D\sim N^d$ ($d$ is spatial dimension) or $D\sim N$ depending on the symmetric feature maps employed. Our results provide a rigorous mathematical foundation for efficient representations of fermionic wavefunctions and enable scalable and systematically improvable neural network solvers for many-electron systems. |
| title | A minimal and universal representation of fermionic wavefunctions (fermions = bosons + one) |
| topic | Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.11431 |