$GW$+2SOSEX self-energy made positive semi-definite
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911062167650304 |
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| author | Bruneval, Fabien Förster, Arno Pavlyukh, Yaroslav |
| author_facet | Bruneval, Fabien Förster, Arno Pavlyukh, Yaroslav |
| contents | The formulation of vertex corrections beyond the $GW$ approximation within the framework of perturbation theory is a subtle and challenging task, which accounts for the wide variety of schemes proposed over the years. Exact self-energies are required to satisfy the mathematical condition of positive semi-definiteness. The $GW$ self-energy fulfills this property, but the vast majority of the vertex-corrected self-energy approximations do not. In this study, we devise a positive semi-definite extension to the $GW$+2SOSEX self-energy that we name $GW$+2SOSEX-psd. To reach this goal, we demonstrate the cancellation of the bare energy poles that are contained in the fully dynamic second-order in $W$ self-energy ($G3W2$). We then demonstrate on molecular examples the correct positive semi-definiteness of the proposed self-energy approximation and its good accuracy in predicting accurate quasiparticle energies for valence and core states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_13293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $GW$+2SOSEX self-energy made positive semi-definite Bruneval, Fabien Förster, Arno Pavlyukh, Yaroslav Chemical Physics Computational Physics The formulation of vertex corrections beyond the $GW$ approximation within the framework of perturbation theory is a subtle and challenging task, which accounts for the wide variety of schemes proposed over the years. Exact self-energies are required to satisfy the mathematical condition of positive semi-definiteness. The $GW$ self-energy fulfills this property, but the vast majority of the vertex-corrected self-energy approximations do not. In this study, we devise a positive semi-definite extension to the $GW$+2SOSEX self-energy that we name $GW$+2SOSEX-psd. To reach this goal, we demonstrate the cancellation of the bare energy poles that are contained in the fully dynamic second-order in $W$ self-energy ($G3W2$). We then demonstrate on molecular examples the correct positive semi-definiteness of the proposed self-energy approximation and its good accuracy in predicting accurate quasiparticle energies for valence and core states. |
| title | $GW$+2SOSEX self-energy made positive semi-definite |
| topic | Chemical Physics Computational Physics |
| url | https://arxiv.org/abs/2507.13293 |