Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912458904436736 |
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| author | Pokhilko, Pavel Zgid, Dominika |
| author_facet | Pokhilko, Pavel Zgid, Dominika |
| contents | Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the homotopy continuation approach to control the behavior of iterations. We used the homotopy continuation to locate multiple fully self-consistent GW solutions for NdNiO2 solid and to establish the corresponding Hartree-Fock limits. Some of the solutions found are qualitatively new and help to understand the nature of electron correlation in this material. We show that there are multiple low-energy charge-transfer solutions leading to a formation of charge-density waves. Our results qualitatively agree with the experimental conductivity measurements. To rationalize the structure of solutions, we compare the k-point occupations and generalize the concept of natural difference orbitals for correlated periodic solids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2 Pokhilko, Pavel Zgid, Dominika Strongly Correlated Electrons Materials Science Superconductivity Chemical Physics Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the homotopy continuation approach to control the behavior of iterations. We used the homotopy continuation to locate multiple fully self-consistent GW solutions for NdNiO2 solid and to establish the corresponding Hartree-Fock limits. Some of the solutions found are qualitatively new and help to understand the nature of electron correlation in this material. We show that there are multiple low-energy charge-transfer solutions leading to a formation of charge-density waves. Our results qualitatively agree with the experimental conductivity measurements. To rationalize the structure of solutions, we compare the k-point occupations and generalize the concept of natural difference orbitals for correlated periodic solids. |
| title | Homotopy continuation method for solving Dyson equation fully self-consistently: theory and application to NdNiO2 |
| topic | Strongly Correlated Electrons Materials Science Superconductivity Chemical Physics |
| url | https://arxiv.org/abs/2507.00290 |