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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19085 |
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| _version_ | 1866911583286853632 |
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| author | Calero-Osorio, Daniel F. Ayers, Paul W. |
| author_facet | Calero-Osorio, Daniel F. Ayers, Paul W. |
| contents | We propose a method to solve the electronic Schrödinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps the Hamiltonian into the seniority-zero space: seniority-zero wavefunctions are computationally simpler, but still capture strong correlation within electron pairs. The unitary rotation is evaluated using the Baker Campbell Hausdorff (BCH) expansion, truncated to two-body operators through the operator decomposition strategy of canonical transformation (CT) theory, which rewrites higher-rank terms approximately in terms of one- and two-body operators. Unlike conventional approaches to CT theory, the generator is chosen to minimize the size of non-seniority-zero elements of the transformed Hamiltonian. Numerical tests reveal that this Seniority-zero Linear Canonical Transformation (SZ-LCT) method delivers highly accurate results, usually with submilliHartree error. The effective computational scaling of SZ-LCT is $\mathcal{O}(N^8/n_c)$ , where $n_c$ is the number of cores available for the computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Seniority-zero Linear Canonical Transformation Theory Calero-Osorio, Daniel F. Ayers, Paul W. Chemical Physics We propose a method to solve the electronic Schrödinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps the Hamiltonian into the seniority-zero space: seniority-zero wavefunctions are computationally simpler, but still capture strong correlation within electron pairs. The unitary rotation is evaluated using the Baker Campbell Hausdorff (BCH) expansion, truncated to two-body operators through the operator decomposition strategy of canonical transformation (CT) theory, which rewrites higher-rank terms approximately in terms of one- and two-body operators. Unlike conventional approaches to CT theory, the generator is chosen to minimize the size of non-seniority-zero elements of the transformed Hamiltonian. Numerical tests reveal that this Seniority-zero Linear Canonical Transformation (SZ-LCT) method delivers highly accurate results, usually with submilliHartree error. The effective computational scaling of SZ-LCT is $\mathcal{O}(N^8/n_c)$ , where $n_c$ is the number of cores available for the computation. |
| title | Seniority-zero Linear Canonical Transformation Theory |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2509.19085 |