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Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains

by Yingfei Gu, Andrew Lucas, Xiao-Liang Qi

Submission summary

As Contributors: Andrew Lucas
Arxiv Link: https://arxiv.org/abs/1702.08462v2 (pdf)
Date accepted: 2017-05-11
Date submitted: 2017-05-10 02:00
Submitted by: Lucas, Andrew
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
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.

Ontology / Topics

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Butterfly effect Diffusion Lyapunov exponents Quantum chaos Sachdev-Ye-Kitaev (SYK) model Spatially inhomogeneous systems Transport

Published as SciPost Phys. 2, 018 (2017)



Author comments upon resubmission

We thank the referees for their positive feedback. We have edited the manuscript along the lines suggested -- see the list of changes. We hope that these changes satisfy the referees and the paper can be published in its present form.

List of changes

1) We have added Reference 12 in the introduction as an example of a violation of a postulated relation between charge diffusion and v_B.

2) We have modified the main text in Section 2 around Equations 7-11, along with adding a new Appendix, in order to address a referee's concern that our derivation of the effective action should be more self-contained.

Submission & Refereeing History

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Resubmission 1702.08462v2 on 10 May 2017

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