RECORD
Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
Strongly Correlated Electrons · Submitted 23 Jun 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
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)].
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.62 | 0.12 | 0.16 | asserted 0.93 |
| s1 | The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. | method 0.94 | 0.15 | 0.07 | asserted 1.00 |
| s2 | A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. | method 0.80 | 0.29 | 0.21 | asserted 1.00 |
| s3 | 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. | contribution 0.93 | 0.56 | 0.11 | asserted 0.92 |
| s4 | We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. | contribution 0.98 | 0.87 | 0.06 | asserted 1.00 |
| s5 | This lecture note follows the Japanese review article with major revisions [H. | background 0.97 | 0.20 | 0.02 | asserted 0.89 |
| s6 | Shinaoka et al., Solid State Physics 56(6), 301 (2021)]. | background 0.98 | 0.06 | 0.02 | unclear 0.72 |
What was examined, and what was not
- arXiv listing abstract v4
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original 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)].
Human review
How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 1 paper
-
For the Matsubara frequencies we used the sparse-sampling approach [ref] of the intermediate representation (IR) basis [ref] with an IR parameter \(Λ=10^4\) and a basis cutoff \(δ_IR=10^-8\).
Doping fingerprints of spin and lattice fluctuations in moir\'e superlattice systems · Numerical details of FLEX calculations · 1.00
Compares with it 1 paper
-
Our presentation of the IR differs from Refs. [ref] in two ways.
Discrete Lehmann representation of imaginary time Green's functions · Intermediate representation · 0.98
Cites it as background 2 papers
-
For an extended review on the IR, we refer the reader to Refs. [ref] and [ref] .
Solving the Bethe-Salpeter equation with exponential convergence · Review: Sparse modeling · 1.00
-
For an overview, see Ref. [ref] .
Two-particle correlations and the metal-insulator transition: Iterated Perturbation Theory revisited · Outlook · 1.00
What it cites · 1 sentence without a confident label
Cites as background 1 paper
-
In addition to those introduced in this section, there are many other applications in the field of ab initio calculations, such as the calculation of the superconducting transition temperature using the FLEX approximation [ref] , ab initio calculations of NiO compounds based on the self-energy embedding method [ref] , and an ab initio estimation of the magnetic interaction constant of NdNiO$_2$ [ref] .
Doping fingerprints of spin and lattice fluctuations in moir\'e superlattice systems · Other applications · 0.80
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.