Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911703996825600 |
|---|---|
| author | Zhang, Min-Ye Lin, Peize Shi, Rong Ren, Xinguo |
| author_facet | Zhang, Min-Ye Lin, Peize Shi, Rong Ren, Xinguo |
| contents | The many-body perturbation theory within the $GW$ approximation is a widely used method for describing the electronic band structures in real materials. Its application to large-scale systems is, however, impeded by its high computational cost. The rate-limiting steps in a typical $GW$ implementation are the evaluation of the polarization function under the random phase approximation (RPA) and the evaluation of the $GW$ self-energy, both of which have a canonical $O(N^4)$ scaling with $N$ being the system size. The conventional space-time algorithm within the plane-wave basis sets reduces the scaling from $O(N^4)$ to $O(N^3)$, albeit with a large prefactor and increased memory cost. Here, we present a space-time algorithm within the numerical atomic orbital (NAO) basis-set framework, for which the evaluation of the polarization function and self-energy is formally reduced to $O(N^2)$ or better with respect to system size. This is achieved by computing these quantities in real space, where low-scaling algorithms can be formulated by leveraging the localized resolution of identity (LRI) technique. The resulting NAO-based, LRI-enhanced space-time $GW$ algorithm has been implemented in the LibRPA library interfaced with the FHI-aims code package. Benchmark calculations for crystalline solids show that the low-scaling implementation yields quasi-particle energies in close agreement with the conventional $O(N^4)$ k-space formalism previously implemented in FHI-aims. For the systems studied here, the observed overall scaling is substantially reduced relative to the canonical approach, and the low-scaling implementation becomes advantageous already for systems containing fewer than 100 atoms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27292 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework Zhang, Min-Ye Lin, Peize Shi, Rong Ren, Xinguo Materials Science The many-body perturbation theory within the $GW$ approximation is a widely used method for describing the electronic band structures in real materials. Its application to large-scale systems is, however, impeded by its high computational cost. The rate-limiting steps in a typical $GW$ implementation are the evaluation of the polarization function under the random phase approximation (RPA) and the evaluation of the $GW$ self-energy, both of which have a canonical $O(N^4)$ scaling with $N$ being the system size. The conventional space-time algorithm within the plane-wave basis sets reduces the scaling from $O(N^4)$ to $O(N^3)$, albeit with a large prefactor and increased memory cost. Here, we present a space-time algorithm within the numerical atomic orbital (NAO) basis-set framework, for which the evaluation of the polarization function and self-energy is formally reduced to $O(N^2)$ or better with respect to system size. This is achieved by computing these quantities in real space, where low-scaling algorithms can be formulated by leveraging the localized resolution of identity (LRI) technique. The resulting NAO-based, LRI-enhanced space-time $GW$ algorithm has been implemented in the LibRPA library interfaced with the FHI-aims code package. Benchmark calculations for crystalline solids show that the low-scaling implementation yields quasi-particle energies in close agreement with the conventional $O(N^4)$ k-space formalism previously implemented in FHI-aims. For the systems studied here, the observed overall scaling is substantially reduced relative to the canonical approach, and the low-scaling implementation becomes advantageous already for systems containing fewer than 100 atoms. |
| title | Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework |
| topic | Materials Science |
| url | https://arxiv.org/abs/2603.27292 |