Spectral properties from an efficient analytical representation of the $GW$ self-energy within a multipole approximation
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| Format: | Preprint |
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2025
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| _version_ | 1866915288153325568 |
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| author | Leon, Dario A. Berland, Kristian Cardoso, Claudia |
| author_facet | Leon, Dario A. Berland, Kristian Cardoso, Claudia |
| contents | We propose an efficient analytical representation of the frequency-dependent $GW$ self-energy $Σ$ via a multipole approximation (MPA-$Σ$). The multipole-Padé model for the self-energy is interpolated from a small set of numerical evaluations of $Σ$ in the complex frequency plane, similarly to the previously multipole representation developed for the screened Coulomb interaction (MPA-$W$) [Phys. Rev. B \textbf{104}, 115157 (2021)]. We show that, likewise MPA-$W$, an appropriate choice of frequency sampling in MPA-$Σ$ is critical to guarantee computational efficiency and high accuracy. The combined MPA-$W$ and MPA-$Σ$ scheme considerably reduces the cost of full-frequency self-energy calculations, especially for spectral band structures over a wide energy range. Crucially, MPA-$Σ$ enables a multipole representation for the interacting Green's function $G$ (MPA-$G$), providing a straightforward evaluation of all the spectral properties, and a more general way to define the renormalization factor $Z$. We validate the MPA-$Σ$ and MPA-$G$ approaches for diverse systems: bulk Si, Na and Cu, monolayer MoS$_2$, the NaCl ion-pair and the F$_2$ molecule. Moreover, we introduce toy MPA-$Σ$/$G$ models to examine the quasiparticle picture in different regimens of weak and strong correlation. With these models, we expose limitations in defining $Z$ from the local derivative of $Σ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_09121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral properties from an efficient analytical representation of the $GW$ self-energy within a multipole approximation Leon, Dario A. Berland, Kristian Cardoso, Claudia Materials Science We propose an efficient analytical representation of the frequency-dependent $GW$ self-energy $Σ$ via a multipole approximation (MPA-$Σ$). The multipole-Padé model for the self-energy is interpolated from a small set of numerical evaluations of $Σ$ in the complex frequency plane, similarly to the previously multipole representation developed for the screened Coulomb interaction (MPA-$W$) [Phys. Rev. B \textbf{104}, 115157 (2021)]. We show that, likewise MPA-$W$, an appropriate choice of frequency sampling in MPA-$Σ$ is critical to guarantee computational efficiency and high accuracy. The combined MPA-$W$ and MPA-$Σ$ scheme considerably reduces the cost of full-frequency self-energy calculations, especially for spectral band structures over a wide energy range. Crucially, MPA-$Σ$ enables a multipole representation for the interacting Green's function $G$ (MPA-$G$), providing a straightforward evaluation of all the spectral properties, and a more general way to define the renormalization factor $Z$. We validate the MPA-$Σ$ and MPA-$G$ approaches for diverse systems: bulk Si, Na and Cu, monolayer MoS$_2$, the NaCl ion-pair and the F$_2$ molecule. Moreover, we introduce toy MPA-$Σ$/$G$ models to examine the quasiparticle picture in different regimens of weak and strong correlation. With these models, we expose limitations in defining $Z$ from the local derivative of $Σ$. |
| title | Spectral properties from an efficient analytical representation of the $GW$ self-energy within a multipole approximation |
| topic | Materials Science |
| url | https://arxiv.org/abs/2501.09121 |