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Many-body quantum dynamics slows down at low density
by Xiao Chen, Yingfei Gu, Andrew Lucas
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Submission summary
| Authors (as registered SciPost users): | Andrew Lucas |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2007.10352v2 (pdf) |
| Date submitted: | 2020-07-28 16:36 |
| Submitted by: | Lucas, Andrew |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-9-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2007.10352v2, delivered 2020-09-29, doi: 10.21468/SciPost.Report.2032
Strengths
1. This is a nice discussion of a physically clear phenomenon: chaos is suppressed at low densities since there are fewer collisions.
2. The inner-product based approach is elegant and fairly transparent, and leads to a simple derivation of density-dependent bounds.
3. The calculations on SYK and Brownian SYK are clear.
Weaknesses
1. I would have liked some cleaner physical motivation of the n^(1/2) dependence in the low density limit. It is clear that the operator size must behave as exp(-c mu) for some constant but this does not fix the exponent. In the limiting case it feels like some more elementary argument should be available and I encourage the authors to lay it out / find it.
Report
I think this paper is interesting and can be published.
Report #1 by Anonymous (Referee 1) on 2020-9-3 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2007.10352v2, delivered 2020-09-03, doi: 10.21468/SciPost.Report.1957
Strengths
1. Clarity of presentation including all definitions
2. Derivation of a sensible result using interesting methods
Report
This work derives bounds on the Lyapunov exponent in the low density limit of quantum systems with U(1) charge conservation. Given that bounds and scaling properties of Lyapunov exponents are hard to explicitly derive, this is a useful contribution. The work is methodical, and language and definitions are made clear. Some small points:
1. "In this paper, we elect to study a simpler analogue of low temperature physics – a system at infinite temperature," Sounds like an oxymoron, so maybe the authors can unpack what they really mean by this statement?
2. Page 3 reference is missing.
3. typo "resultt" on page 7.