SciPost Submission Page
Multi-orbital two-particle self-consistent approach -- strengths and limitations
by Jonas B. Profe, Jiawei Yan, Karim Zantout, Philipp Werner, Roser Valentí
Submission summary
| Authors (as registered SciPost users): | Jonas Profe |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2410.00962v6 (pdf) |
| Date submitted: | April 17, 2025, 9:45 a.m. |
| Submitted by: | Profe, Jonas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Extending many-body numerical techniques which are powerful in the context of simple model calculations to the realm of realistic material simulations can be a challenging task. Realistic systems often involve multiple active orbitals, which increases the complexity and numerical cost because of the large local Hilbert space and the large number of interaction terms or sign-changing off-diagonal Green's functions. The two-particle self-consistent approach (TPSC) is one such many-body numerical technique, for which multi-orbital extensions have proven to be involved due to the substantially more complex structure of the local interaction tensor. In this paper we extend earlier multi-orbital generalizations of TPSC by setting up two different variants of a fully self-consistent theory for TPSC in multi-orbital systems. We first investigate the strengths and limitations of the approach analytically and then benchmark both variants against dynamical mean-field theory (DMFT) and D-TRILEX results. We find that the exact behavior of the system can be faithfully reproduced in the weak-coupling regime, while at stronger couplings the performance of the two TPSC variants strongly depends on details of the system.
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
List of changes
See redlined manuscript in comment to referee 1
Current status:
Reports on this Submission
Report #1 by Camille Lahaie (Referee 2) on 2025-5-5 (Invited Report)
Strengths
This paper shows how to solve a multi-orbital Hubbard system with SU(2) symmetry with TPSC. This is a great addition to the domain as TPSC has been known to show physical features inaccessible to Dynamical mean-field calculations or Monte-Carlo ones.
The derivations are thorough and well explained, and the author added many details in Appendices, which are all really pertinent.
The analysis of the limits of the Hartree-Fock decoupling is really interesting and gives insights to the limitations of TPSC in its pure form.
The method is benchmarked against a previous formulation of multi-orbital TPSC, DMFT and D-TRILEX
Weaknesses
The train of thoughts in the benchmark section can be hard to follow, however, I think this is not an issue that can easily be resolved, and the paper has still proven to be consistent.
There are still some typos.
Report
I thank the authors for the first two replies of the first and second submission.
I have followed the redprint for my comments. It was discussed with André-Marie Tremblay.
The two-particle self-consistent approach (TPSC) is an appealing method to study strongly correlated systems. It satisfies many exact results and even though multi-orbital formulations were already done before, this generalisation in the SU(2) symmetry which is presented in this paper is non trivial and will be a great addition to the field.
I think publication can be recommended only after the authors modify the small changes and answer some questions.
Requested changes
1- (Question) In Sec 3: After eqs 48, 49 and 50, that show the values of the 3 vertices of TPSC as a function of U and J of the Kanamori model. We see that the right-hand side of eqs 49 and 50 are equal, does that also mean automatically that P=C? I would expect that this is not the case for TPSC5, right?
2- In Eq 51: Shouldn’t there be a sum over k and ν? Or maybe we used Einstein’s notation and I missed the comment? But I also think there should be a normalisation term here?
3- Eq 52: One U should be U'? It is mentioned below that equation that U=U', so perhaps U' should appear in that equation. Or maybe looking at the Kanamori model, they should not be separated as such and just mentioning their properties (intra- or inter- orbital) is enough. I am just asking to make sure it is also clear for readers.
4- One suggestion, it is up for the authors, but I think readers would be more inclined to follow the discussion if the comparisons to DMFT were done before the isolated case of J=0 discussion, which shows and explains why TPSC fails at low J and not so much at higher J. (So Sec 3.2 before Sec 3.1) But I do understand in a way why it was done the way it is right now. So I leave it to the authors to decide.
5- After Eq 59: I think there is a typo, the sentence starts with “This we can …”.
6- In the caption of the plots of Figure 3 : I think the number of the Reference was not updated, because it is not the same as in the citation of the same figure.
7- Last paragraph of Sec. 3.3.2 : There is no direct reference to the figure that shows susceptibilities (Fig 6, I think) , even though there is a discussion about it. This seems to be just an oversight.
8- Figure 2b) : From what type of calculation do those results come from? Exact diagonalization, DMFT?
9- In Section 3.2 : There is an explanation of the limitation of TPSC at low temperature coming from the Hartree-Fock decoupling, but then in Appendix E, it is said that Hartree Fock is more valid at low temperature, this looks like a contradiction. After a couple of re-reading, I have come to understand that the limitation at low temperature for TPSC is due to the importance of the non-local and non-static corrections on the vertices, but doesn’t that also apply to Hartree-Fock?
Recommendation
Publish (meets expectations and criteria for this Journal)