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Physical and unphysical regimes of self-consistent many-body perturbation theory
by Kris Van Houcke, Evgeny Kozik, Riccardo Rossi, Youjin Deng, Félix Werner
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Submission summary
| Authors (as registered SciPost users): | Youjin Deng · Félix Werner |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202102_00011v2 (pdf) |
| Date submitted: | 2024-03-27 15:03 |
| Submitted by: | Werner, Félix |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $\mathcal{N}$ and plugged into the Dyson equation, which is then solved for the propagator $G_{\mathcal{N}}$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_{\mathcal{N}}$ converges when $\mathcal{N}\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}$ at small enough coupling, while $G_\infty \neq G_{\rm exact}$ at strong coupling. This follows from the findings of~[Kozik, Ferrero and Georges, PRL {\bf 114}, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}$ and $G_\infty\neq G_{\rm exact}$ regimes thanks to a criterion which does not require the knowledge of $G_{\rm exact}\,$, as proposed in [Rossi et al., PRB {\bf 93}, 161102(R) (2016)].
Author comments upon resubmission
reply.pdf
manuscript_marked_changes.pdf
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https://drive.google.com/drive/folders/1hXSIMyShQfiDlJMMofX7C5Op7KFrJxUl?
List of changes
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Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 3) on 2024-4-9 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202102_00011v2, delivered 2024-04-09, doi: 10.21468/SciPost.Report.8856
Strengths
No changes compared to the previous report.
Weaknesses
The two main weaknesses I emphasized in the previous report have been resolved by revision.
Report
The authors make improvements to the manuscript and address the comments of the Referees.
The two main criticisms by the Referees were:
1) only reading the text, one cannot clearly understand what the progress is that is made in the manuscript
2) the criterion for detecting misleading convergence (Eq.9) is not derived in the paper
The authors address both of these criticisms. They add some additional explanations of what is actually new in the present work. In my opinion, the paper presents a reasonable amount of new results, and I expect the paper to be useful to people employing BDMC. The authors also provide a short derivation of Eq.9 in the appendix. I find no issues with the proof, but I feel like one could improve the presentation by adding a few sentences at the end to connect the proof more explicitly with the written statements Eq.9 and Eq.10.
The authors also address the minor criticisms of the Referees. Most importantly, the authors elaborate and give guidelines on how to choose \xi when applying the test for misleading convergence.
In general I think that the manuscript is in good shape, and I recommend the publication of the manuscript in SciPost Physics. In my opinion, the paper satisfies the acceptance criterion "Open a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work". The paper does not solve the issue of misleading convergence of the self-energy in BDMC methods, but it is equally important to be able to distinguish between correct and incorrect results, and this paper will definitely help with that.
Recommendation
Publish (meets expectations and criteria for this Journal)