SciPost Submission Page
Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods
by Raphaël Photopoulos, Antoine Boulet
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Antoine Boulet · Raphaël Photopoulos |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2402.17627v2 (pdf) |
| Date submitted: | 2024-05-17 14:23 |
| Submitted by: | Boulet, Antoine |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schr\"odinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
See Report
Weaknesses
see Report
Report
Report on
“Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods”
by Raphaël Photopoulos and Antoine Boulet
The authors, R. Photopoulos and A. Boulet develop a strategy for applying many-body perturbation theory starting from an effective Hamiltonian that already contains correlations beyond the mean-field level. In particular, their method provides a solution to the over-counting of correlations that is known to be inherent in this type of approach.
Overall, this work is clear, well presented and well written. Several examples are presented and compared to exact results in order to illustrate the validity and accuracy of their theoretical method.
I would now like to make a few comments on specific points raised in the manuscript.
1- In order to discuss the validity of their theoretical approach, the authors focus essentially on the ground-state energy as a function of the relevant physical parameter of the many-body Hamiltonian under consideration. However, in several illustrative models considered in their study, other relevant quantities such as correlation functions could be calculated. This would allow a better assessment of how close the N-body ground-state calculated in their approach is to the exact many-body ground state. It is as well possible to calculate directly the overlap between the exact ground state and the one they calculate in their MBPT approach. For instance, this could be achieved relatively easily in the case of the four-site Hubbard model and even in the case of the Richardson pairing Hamiltonian.
2- In Fig.4, which concerns the case of the one-dimensional Hubbard chain, the calculations corresponding to l=2 (third order perturbation) are not shown, why? The authors should present the results the agreement should be better than for l=1?
3- In the case of Hubbard's four-site model, it would appear, in the attractive case, that agreement decreases as the order of perturbation increases. For example, the agreement between the exact calculations and the MBPT calculations for l=0 is excellent, whereas as the order of perturbation increases, it decreases. Do the authors have an explanation?
4- In Figures 1, 4 and 5, the left and right panels (a) and (b) are the same data plotted as a function of the relevant parameter or its inverse. In my opinion, the authors should choose one of them. There's no need to keep both, there's no advantage in doing so, it doesn't help to better understand their results and the comparison between the exact calculations and MBPT calculations.
Recommendation
Ask for minor revision
Author: Antoine Boulet on 2024-11-04 [id 4931]
(in reply to Report 2 on 2024-10-05)Dear Editor, Dear Reviewers,
We would like to thank you for your time in reviewing our paper and providing valuable comments that led to possible improvements in the current version. We have carefully considered the comments and tried our best to address every one of them. We hope that the manuscript after careful revisions, will meet your high standards. We welcome further constructive comments if any. In attachment, we provide the point-by-point responses.
Sincerely,
R. Photopoulos and A. Boulet
Attachment:
response_2.pdf