Graph-based block-diagonalization of full configuration interaction Hamiltonian: H$_2$ chains study
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912513304559616 |
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| author | Park, Hayun Lee, Hunpyo |
| author_facet | Park, Hayun Lee, Hunpyo |
| contents | We developed a graph-based block-diagonalization (GBBD) method for the full configuration interaction Hamiltonian of molecular systems to efficiently calculate the exact eigenvalues of low-energy states. In this approach, the non-zero matrix elements of the Hamiltonian are represented as edges on a graph, which naturally decomposes into disconnected clusters. Each cluster corresponds to an independent block in the block-diagonalized form of the Hamiltonian. The eigenvalues in the low-energy sector were obtained by solving the eigenvalue problem for each block matrix and by solving a modified Hamiltonian subject to orthonormality constraints with respect to previously computed lower-energy eigenstates. We applied the GBBD method to linear hydrogen H chains ranging from H$_2$ to H$_{12}$. The results showed excellent agreement with exact ones, confirming both the accuracy and efficiency of the proposed method. Finally, we discussed several physical properties with respect to the number of H$_2$ molecules. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_23593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph-based block-diagonalization of full configuration interaction Hamiltonian: H$_2$ chains study Park, Hayun Lee, Hunpyo Chemical Physics Strongly Correlated Electrons Quantum Physics We developed a graph-based block-diagonalization (GBBD) method for the full configuration interaction Hamiltonian of molecular systems to efficiently calculate the exact eigenvalues of low-energy states. In this approach, the non-zero matrix elements of the Hamiltonian are represented as edges on a graph, which naturally decomposes into disconnected clusters. Each cluster corresponds to an independent block in the block-diagonalized form of the Hamiltonian. The eigenvalues in the low-energy sector were obtained by solving the eigenvalue problem for each block matrix and by solving a modified Hamiltonian subject to orthonormality constraints with respect to previously computed lower-energy eigenstates. We applied the GBBD method to linear hydrogen H chains ranging from H$_2$ to H$_{12}$. The results showed excellent agreement with exact ones, confirming both the accuracy and efficiency of the proposed method. Finally, we discussed several physical properties with respect to the number of H$_2$ molecules. |
| title | Graph-based block-diagonalization of full configuration interaction Hamiltonian: H$_2$ chains study |
| topic | Chemical Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2507.23593 |