SciPost Submission Page
Two-particle self-consistent approach for broken symmetry phases
by Lorenzo Del Re
Submission summary
| Authors (as registered SciPost users): | Lorenzo Del Re |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202407_00001v3 (pdf) |
| Date submitted: | 2024-11-14 17:44 |
| Submitted by: | Del Re, Lorenzo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Spontaneous symmetry breaking of interacting fermion systems constitutes a major challenge for many-body theory due to the proliferation of new independent scattering channels once absent or degenerate in the symmetric phase. One example is given by the ferro/antiferromagnetic broken symmetry phase (BSP) of the Hubbard model, where vertices in the spin-transverse and spin-longitudinal channels become independent with a consequent increase in the computational power for their calculation. Here we generalize the formalism of the non-perturbative Two-Particle-Self-Consistent method (TPSC) to treat broken SU(2) magnetic phases of the Hubbard model, providing with a efficient yet reliable method. We show that in the BSP, the sum-rule enforcement of susceptibilities must be accompanied by a modified gap equation resulting in a renormalisation of the order parameter, vertex corrections and the preservation of the gap-less feature of the Goldstone modes. We then apply the theory to the antiferromagnetic phase of the Hubbard model in the cubic lattice at half-filling. We compare our results of double occupancies and staggered magnetisation to the ones obtained using Diagrammatic Monte Carlo showing excellent quantitative agreement. We demonstrate how vertex corrections play a central role in lowering the Higgs resonance with respect to the quasi-particle excitation gap in the spin-longitudinal susceptibility, yielding a well visible Higgs-mode.
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
Author comments upon resubmission
Thank you for inviting new referees and providing their reports. We appreciate the referees' careful, positive, and constructive feedback, which has helped us better highlight the potential (and limitations) of the proposed method.
We have provided point-by-point responses to all referees' comments and requests, and we have added the additional data requested by Referee 2.
Given the substantial improvements made to address all comments and requests, we believe the revised version of our paper is now suitable for publication in SciPost Physics.
List of changes
We have attached the complete response to all referees, along with a diff file comparing the previous and updated versions of the manuscript, available on the dialog page for report #1.
Current status:
Reports on this Submission
Report
I would like to thank the Author for considering my suggestions and for performing additional calculations in the revised version of the manuscript. I would be happy to recommend the publication of this work in SciPost Physics provided the Author addresses two remaining issues:
1. In their reply to my first question regarding the reliability of the method, the Author mentions that there are no diagrammatic Monte Carlo data available for comparison at higher temperatures. However, the Author did not comment on the possibility of comparing the results of the developed TPSC method to those obtained using the dynamical vertex approximation or other method. Therefore, as I pointed out in the previous review round, the manuscript still does not provide sufficient information to conclusively evaluate the reliability of the method, as claimed in the Abstract. In this regard, the claim of reliability should be removed from the Abstract unless the Author provides a clear and sufficient justification.
2. Regarding my previous question (5), I am surprised to read that the Author has limited their theoretical method development to a half-filled bipartite lattice, which is rarely realized in actual materials. While I understand that this particular case significantly simplifies the implementation of the method and the numerical calculations, I strongly believe that the Author should at least derive the method for a general case and present the corresponding equations without relying on the particle-hole symmetry specific to the half-filled bipartite case.
Recommendation
Ask for minor revision
Report #2 by Nicolas Martin (Referee 4) on 2024-11-29 (Invited Report)
Report
The modifications to the manuscript have addressed in a satisfactory manner all the points raised by referees. I believed the revised version should be published in SciPost Physics.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
The author answered satisfactorily to all open points by the referees and I recommend publication of the submitted revised manuscript
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)