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

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

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Submission summary

Authors (as registered SciPost users): Hiroshi Shinaoka
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-07-20
Date submitted: 2022-06-10 08:33
Submitted by: Shinaoka, Hiroshi
Submitted to: SciPost Physics Lecture Notes
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


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)].

Published as SciPost Phys. Lect. Notes 63 (2022)

Author comments upon resubmission

Dear the editors,

Thank you for forwarding the all-in-all very positive referee reports with constructive suggestions. Although we were asked for only a minor revision, we unexpectedly decided to upgrade the Python library described in the manuscript. We apologize for the late response, as we had to wait for that.

We answer in detail all points raised by the referees.
We summarize the major updates in the list of changes below.
We believe our manuscript has largely profited from the referees' suggestions
and that the revised version is now suitable for publication.

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

List of changes

* The notation in Section 2 has been changed for consistency with the new Python library ``sparse-ir'' The kernel is now defined in imaginary time rather than Matsubara frequency.
* For a comparison with related approaches, we have extended Sec. 3.4 and added a new subsection 3.5 (comment #1 of the first Referee). A new figure (Fig. 6) has been added.
* The description of the Python library and sample codes have been updated for the new Python library ``sparse-ir''.
* Minor revisions to improve the readability have been made.

Reports on this Submission

Anonymous Report 1 on 2022-6-23 (Invited Report)


1. Authors have updated the text with a comparison to related approaches
2. Authors have upgraded the numerical library described in the manuscript


Nothing in particular


I think the authors have made a proper job in the resubmission and I can recommend the paper for publication.

  • validity: top
  • significance: high
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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