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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2506.00155 |
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| _version_ | 1866908557649117184 |
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| author | Zhan, Ni Wheeler, William A. Goldshlager, Gil Ertekin, Elif Adams, Ryan P. Wagner, Lucas K. |
| author_facet | Zhan, Ni Wheeler, William A. Goldshlager, Gil Ertekin, Elif Adams, Ryan P. Wagner, Lucas K. |
| contents | Neural network wave functions have shown promise as a way to achieve high accuracy on the many-body quantum problem. These wave functions most commonly use a determinant or sum of determinants to antisymmetrize many-body orbitals which are described by a neural network. In many cases, the wave function is projected onto a fixed-spin state. Such a treatment is allowed for spin-independent operators; however, it cannot be applied to spin-dependent problems, such as Hamiltonians containing spin-orbit interactions. We show that for spin-independent Hamiltonians, a strict upper bound property is obeyed between a traditional Hartree-Fock like determinant, full spinor wave function, the full determinant wave function, and a generalized spinor wave function. The relationship between a spinor wave function and the full determinant arises because the full determinant wave function is the spinor wave function projected onto a fixed-spin, after which antisymmetry is implicitly restored in the spin-independent case. For spin-dependent Hamiltonians, the full determinant wave function is not applicable, because it is not antisymmetric. Numerical experiments on the H$_3$ molecule and two-dimensional homogeneous electron gas confirm the bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expressivity of determinantal ansatzes for neural network wave functions Zhan, Ni Wheeler, William A. Goldshlager, Gil Ertekin, Elif Adams, Ryan P. Wagner, Lucas K. Strongly Correlated Electrons Neural network wave functions have shown promise as a way to achieve high accuracy on the many-body quantum problem. These wave functions most commonly use a determinant or sum of determinants to antisymmetrize many-body orbitals which are described by a neural network. In many cases, the wave function is projected onto a fixed-spin state. Such a treatment is allowed for spin-independent operators; however, it cannot be applied to spin-dependent problems, such as Hamiltonians containing spin-orbit interactions. We show that for spin-independent Hamiltonians, a strict upper bound property is obeyed between a traditional Hartree-Fock like determinant, full spinor wave function, the full determinant wave function, and a generalized spinor wave function. The relationship between a spinor wave function and the full determinant arises because the full determinant wave function is the spinor wave function projected onto a fixed-spin, after which antisymmetry is implicitly restored in the spin-independent case. For spin-dependent Hamiltonians, the full determinant wave function is not applicable, because it is not antisymmetric. Numerical experiments on the H$_3$ molecule and two-dimensional homogeneous electron gas confirm the bounds. |
| title | Expressivity of determinantal ansatzes for neural network wave functions |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2506.00155 |