Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

Shinaoka, Hiroshi; Chikano, Naoya; Gull, Emanuel; Li, Jia; Nomoto, Takuya; Otsuki, Junya; Wallerberger, Markus; Wang, Tianchun; Yoshimi, Kazuyoshi

doi:10.21468/SciPostPhysLectNotes.63

SciPost Physics Lecture Notes

Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

Hiroshi Shinaoka, Naoya Chikano, Emanuel Gull, Jia Li, Takuya Nomoto, Junya Otsuki, Markus Wallerberger, Tianchun Wang, Kazuyoshi Yoshimi

SciPost Phys. Lect. Notes 63 (2022) · published 22 September 2022

doi: 10.21468/SciPostPhysLectNotes.63
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Abstract

This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal-Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article with major revisions [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.63
TI  - Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
PY  - 2022/09/22
UR  - https://www.scipost.org/SciPostPhysLectNotes.63
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 63
A1  - Shinaoka, Hiroshi
AU  - Chikano, Naoya
AU  - Gull, Emanuel
AU  - Li, Jia
AU  - Nomoto, Takuya
AU  - Otsuki, Junya
AU  - Wallerberger, Markus
AU  - Wang, Tianchun
AU  - Yoshimi, Kazuyoshi
AB  - This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal-Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article with major revisions [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].
ER  -

@Article{10.21468/SciPostPhysLectNotes.63,
	title={{Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function}},
	author={Hiroshi Shinaoka and Naoya Chikano and Emanuel Gull and Jia Li and Takuya Nomoto and Junya Otsuki and Markus Wallerberger and Tianchun Wang and Kazuyoshi Yoshimi},
	journal={SciPost Phys. Lect. Notes},
	pages={63},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.63},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.63},
}

Cited by 5

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Hiroshi Shinaoka,
¹ Naoya Chikano,
² Emanuel Gull,
² Jia Li,
³ Takuya Nomoto,
⁴ Junya Otsuki,
⁵ Markus Wallerberger,
³ Tianchun Wang,
³ Kazuyoshi Yoshimi

Funders for the research work leading to this publication

Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
Japan Science and Technology Agency [JST]
日本学術振興会 / Japan Society for the Promotion of Science [JSPS]
Simons Foundation