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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2404.16453 |
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| _version_ | 1866914770288902144 |
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| author | Lani, Giovanna Marzari, Nicola |
| author_facet | Lani, Giovanna Marzari, Nicola |
| contents | We investigate analytically the performance of many-body energy functionals, derived respectively by Klein and Luttinger and Ward, at different levels of diagrammatic approximations, ranging from second Born, to GW, to the so-called T-matrix, for the calculation of total energies and potential energy surfaces. We benchmark our theoretical results on the extended two-site Hubbard model, which is analytically solvable and for which several exact properties can be calculated. Despite its simplicity, this model displays the physics of strongly correlated electrons: it is prototypical of the H$_2$ dissociation, a notoriously difficult problem to solve accurately for the majority of mean-field based approaches. We show that both functionals exhibit good to excellent variational properties, particularly in the case of the Luttinger-Ward one, which is in close agreement with fully self-consistent calculations, and elucidate the relation between the accuracy of the results and the different input one-body Green's functions. Provided that these are wisely chosen, we show how the Luttinger-Ward functional can be used as a computationally inexpensive alternative to fully self-consistent many-body calculations, without sacrificing the precision of the results obtained. Furthermore, in virtue of this accuracy, we argue that this functional can also be used to rank different many-body approximations at different regimes of electronic correlation, once again bypassing the need for self-consistency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Potential energy surfaces from many-body functionals: analytical benchmarks and conserving many-body approximations Lani, Giovanna Marzari, Nicola Strongly Correlated Electrons We investigate analytically the performance of many-body energy functionals, derived respectively by Klein and Luttinger and Ward, at different levels of diagrammatic approximations, ranging from second Born, to GW, to the so-called T-matrix, for the calculation of total energies and potential energy surfaces. We benchmark our theoretical results on the extended two-site Hubbard model, which is analytically solvable and for which several exact properties can be calculated. Despite its simplicity, this model displays the physics of strongly correlated electrons: it is prototypical of the H$_2$ dissociation, a notoriously difficult problem to solve accurately for the majority of mean-field based approaches. We show that both functionals exhibit good to excellent variational properties, particularly in the case of the Luttinger-Ward one, which is in close agreement with fully self-consistent calculations, and elucidate the relation between the accuracy of the results and the different input one-body Green's functions. Provided that these are wisely chosen, we show how the Luttinger-Ward functional can be used as a computationally inexpensive alternative to fully self-consistent many-body calculations, without sacrificing the precision of the results obtained. Furthermore, in virtue of this accuracy, we argue that this functional can also be used to rank different many-body approximations at different regimes of electronic correlation, once again bypassing the need for self-consistency. |
| title | Potential energy surfaces from many-body functionals: analytical benchmarks and conserving many-body approximations |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2404.16453 |