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Many-body quantum dynamics slows down at low density

by Xiao Chen, Yingfei Gu, Andrew Lucas

Submission summary

As Contributors: Andrew Lucas
Arxiv Link: (pdf)
Date accepted: 2020-11-10
Date submitted: 2020-10-15 02:47
Submitted by: Lucas, Andrew
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.

Published as SciPost Phys. 9, 071 (2020)

Author comments upon resubmission

Dear editor/referees,

We thank you for the very positive reports. We have made the minor requested changes to our manuscript and believe it is now ready for publication.

Xiao, Yingfei, Andy

List of changes

Response to the first referee:

We have fixed the typos that were pointed out, and modified the discussion above (1.4) to clarify what we meant by finite density at infinite T as an “analogue” of finite T: both correspond to dynamics in a very small part of Hilbert space.

Response to the second referee:

We added a new paragraph to the introduction (containing equations (1.6) and (1.7)) which explains why (1.5) is a universal bound at finite density.

Another tiny change:

In our discussion of the Schwinger-Keldysh formalism, we changed "world index" to "contour index" since the latter appears more customary in the literature.

Reports on this Submission

Anonymous Report 2 on 2020-11-4 Invited Report


I thank the authors for answering my question, and now recommend publication.

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Anonymous Report 1 on 2020-11-3 Invited Report


The author's have added clarifications as I had requested. I am satisfied and recommend for publication.

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