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Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
by Yingfei Gu, Andrew Lucas, Xiao-Liang Qi
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Submission summary
| Authors (as registered SciPost users): | Andrew Lucas |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1702.08462v1 (pdf) |
| Date submitted: | 2017-03-03 01:00 |
| Submitted by: | Lucas, Andrew |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We compute the energy diffusion constant $D$, Lyapunov time $\tau_{\text{L}}$ and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupled Majorana Sachdev-Ye-Kitaev (SYK) models in the large $N$ and strong coupling limit. We find $D\le v_{\text{B}}^2 \tau_{\text{L}}$ from a combination of analytical and numerical approaches. Our example necessitates the sharpening of postulated transport bounds based on quantum chaos.
Current status:
Reports on this Submission
Anonymous Report 2 on 2017-4-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1702.08462v1, delivered 2017-04-24, doi: 10.21468/SciPost.Report.117
Strengths
1) The paper considers the interesting question of a possible relation between diffusion and chaos in the context of SYK chains. Even though this has been asked before in the context of SYK, the authors generalise previous results to account for site dependent statistics for the random coupling constants of the model.
2) In this generalised setup, the authors derive the effective action (7) for the collective bilocal field. This can be useful for other researchers working on similar topics.
Weaknesses
1) It would be beneficial for the reader to see the logic behind deriving the effective action (10) for the reparametrisation modes. This is a central result which the authors use in order to discuss diffusion in the given model. It is true that the paper is very close to [33] but more details would be useful for the reader.
Report
The authors consider the question of a possible connection between chaos and diffusion in the context of a model which is a generalisation of the SYK model. I find the question and the conclusions of the paper interesting. This is an interesting paper which is certainly worth considering for publication.
Requested changes
1) -
Report 1 by Moshe Rozali on 2017-4-4 (Invited Report)
- Cite as: Moshe Rozali, Report on arXiv:1702.08462v1, delivered 2017-04-04, doi: 10.21468/SciPost.Report.104
Strengths
The relation between chaos and transport in quantum many body systems is an interesting and important subject. The manuscript is concerned with the status of a particular conjectured relation between the two. That conjecture already has some counter-examples, and might be puzzling because the measure of chaos they use has to do with short times whereas the diffusion probes the system's dynamics on longer time scales. Nevertheless, it is clarifying to concretely calculate the conjectured quantities in some specific examples and discuss the putative relation between them. This short paper does that, it is clear and well-written and I recommend publication.
Weaknesses
n/a
Report
n/a
Requested changes
none.