Potential energy surfaces from many-body functionals: Analytical benchmarks and conserving many-body approximations
We investigate analytically the performance of many-body energy functionals, derived by Klein, 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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.043304 |
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| Summary: | We investigate analytically the performance of many-body energy functionals, derived by Klein, 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 we 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. |
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| ISSN: | 2643-1564 |