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Nevanlinna.jl: A Julia implementation of Nevanlinna analytic continuation
by Kosuke Nogaki, Jiani Fei, Emanuel Gull, Hiroshi Shinaoka
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Kosuke Nogaki |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2302.10476v2 (pdf) |
| Code repository: | https://github.com/SpM-lab/Nevanlinna.jl |
| Date accepted: | 2023-10-16 |
| Date submitted: | 2023-09-20 07:19 |
| Submitted by: | Nogaki, Kosuke |
| Submitted to: | SciPost Physics Codebases |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and, by construction, preserves the causality of a response function. For theoretical calculations without statistical noise, this continuation method is a powerful tool to extract real-frequency information from numerical input data on the Matsubara axis. This method has been applied to first-principles calculations of correlated materials. This paper presents its efficient and full-featured open-source implementation of the method including the Hamburger moment problem and smoothing.
Author comments upon resubmission
Author comments upon resubmission
We sincerely thank you for sharing the highly positive feedback from the referees. We are thrilled to learn that our library is recognized as a valuable contribution to the community by both referees. We have individually addressed their comments and made extensive revisions to our manuscript based on their suggestions and feedback. We trust that our revised manuscript now adheres to the publication standards of SciPost Physics Codebases.
List of changes
##### List of changes
1. We have implemented a command-line interface and explained its usage in Section 3.2.2 of our revised manuscript.
2. The revised manuscript now includes a discussion on the rigorous criterion for positive definiteness in both Section 2.2.3 and Section 4.
3. Figure 1 of the manuscript has been updated to include six examples of Nevanlinna analytic continuation.
4. In Section 3.3, we have added a discussion on the challenging Hubbard gap model, which is presented by Figure 3.
5. We have added references [56], [66], and [67] to the reference list.
6. To enhance clarity, the sample code has been moved to Appendix B for easy reference.
7. We have cleaned the notebooks in our repository.
Published as SciPost Phys. Codebases 19 (2023) , SciPost Phys. Codebases 19-r1.0 (2023)
Reports on this Submission
Strengths
1 - an open source implementation of the Nevanlinna analytic continuation algorithm, which is relative new to the community and should be the method of choice for certain examples. This will be very valuable to the community
2 - various representative examples illustrate the algorithm and the package
3 - a clear description of the algorithm
Weaknesses
none
Report
I am satisfied with the changes in the repository and the manuscript.
Requested changes
none
Report #1 by Anonymous (Referee 3) on 2023-9-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2302.10476v2, delivered 2023-09-25, doi: 10.21468/SciPost.Report.7866
Strengths
- The paper and the software address an issue that has plagued the quantum Monte Carlo community for years and the authors have applied theory that exploits the analytic structure of the Matsubara Green's function to improve the state of affairs.
- All the work and the obtained experiences have been made available to the public in a software package.
Weaknesses
- Opportunities for improvements have been taken.
Report
This is a very valuable contribution to the scipost codebases journal and I recommend publication after another round of proof-reading.
Requested changes
3 Usage
3.1 Installation
Firstly, users need to install Julia (v1.6 or newer) and make sure to add the location of the Julia executable (julia) "to your PATH environment variable."
-> "to their PATH environment variable."