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Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
by Yingfei Gu, Andrew Lucas, Xiao-Liang Qi
This is not the latest submitted version.
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: | March 3, 2017, 1 a.m. |
| Submitted by: | Andrew Lucas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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
Report #2 by Anonymous (Referee 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
Requested changes
1) -
Report #1 by Moshe Rozali (Referee 1) 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
Weaknesses
Report
Requested changes
none.