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Simulating the interplay of dipolar and quadrupolar interactions in NMR by spin dynamic mean-field theory
by Timo Gräßer, Götz S. Uhrig
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Timo Gräßer · Götz S. Uhrig |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2507.17720v3 (pdf) |
| Date submitted: | Oct. 30, 2025, 6:56 a.m. |
| Submitted by: | Timo Gräßer |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The simulation of nuclear magnetic resonance (NMR) experiments is a notoriously difficult task, if many spins participate in the dynamics. The recently established dynamic mean-field theory for high-temperature spin systems (spinDMFT) represents an efficient yet accurate method to deal with this scenario. SpinDMFT reduces a complex lattice system to a time-dependent single-site problem, which can be solved numerically with small computational effort. Since the approach retains local quantum degrees of freedom, a quadrupolar term can be exactly incorporated. This allows us to study the interplay of dipolar and quadrupolar interactions for any parameter range, i.e., without the need for a perturbative treatment. We highlight the relevance of local quantum effects by a comparison with the classical analogue 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
Author comments upon resubmission
List of changes
Current status:
Reports on this Submission
Report
In particular, the main criticism of a lack of comparison to other numerical techniques or experiments has been addressed by adding a section on the comparison to experimental FID spectra measured for an AlN single crystal. Whereas the simulated spectra of the ${}^{14}$N spins are in excellent agreement with experiment, some features in the FID spectra of the ${}^{27}$Al spins are less well reproduced. Possible reasons for these deviations are given and discussed. Overall, the added section about the application of spin-DMFT to a real material validates the approach and shows its versatility.
I recommend the manuscript in its current form (v4) for publication in SciPost Physics.
Requested changes
The authors might want to add a sentence in the caption of Figures 7 and 8 introducing the notation $\delta$ for the (chemical) shift.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
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The paper successfully extends spinDMFT to include quadrupolar interactions, providing an efficient and fully quantum framework for simulating NMR spin dynamics in systems with S>1/2.
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The presentation is systematic, supported by clear figures, quantitative analyses, and openly available code, ensuring transparency and accessibility.
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The results demonstrate how quadrupolar terms alter relaxation and line shapes, highlighting the limits of classical approximations and establishing a foundation for future realistic NMR modeling.
Weaknesses
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The inclusion of a local quadrupolar term, while useful, is a natural and technically straightforward extension of previous spinDMFT work rather than a conceptual breakthrough.
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The results are not benchmarked against exact diagonalization, hybrid simulations, or experimental data, leaving the quantitative accuracy of the approach untested.
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The analysis is restricted to homogeneous systems at infinite temperature, without exploring finite-temperature effects, multi-species systems, or experimental comparisons that would broaden its impact.
Report
Requested changes
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Include a short comparison—numerical or qualitative—with known results or experimental trends.
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Add one or two sentences on possible future applications or extensions.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Timo Gräßer on 2025-11-27 [id 6083]
(in reply to Report 1 on 2025-11-07)General reply:
We thank the Referee for thoroughly reading our manuscript and for the constructive comments. We are very glad about the positive feedback and recommendation for publication in SciPost Physics. We understand the Referee's concern regarding the lack of a qualitative comparison of our data to experiment. This was also the main point of criticism of the first Referee reading our manuscript. We decided to include a corresponding section.
1. requested change:
Include a short comparison-numerical or qualitative-with known results or experimental trends.
Reply:
We decided for a direct comparison with experimental data for monocrystalline aluminium nitride (AlN). This system is a bit more complicated than the basic model we considered before, since it contains different nuclear spin species. However, the extension of the self-consistency problem is relatively simple and the numerical implementation straightforward. Moreover, the resulting data agree excellently with the experimental ones. We are convinced that this comparison strongly validates our method and demonstrates its versatility.
Action taken:
We added a new section 4 containing an extension of the model and comparison to experimental data for AlN.
2. requested change:
Add one or two sentences on possible future applications or extensions.
Reply:
The results for AlN support spinDMFT as a prediction tool for determining dipolar broadening of quadrupolar lines.
Action taken:
We added a sentence about this in the abstract and conclusion.