Many-body quantum dynamics slows down at low density

• URL: http://arxiv.org/abs/2007.10352v3
• Date: Wed, 14 Oct 2020 16:20:07 GMT
• Title: Many-body quantum dynamics slows down at low density
• Authors: Xiao Chen, Yingfei Gu, Andrew Lucas
• Abstract summary: We study quantum many-body systems with a global U(1) conservation law. We define an effective operator size at finite chemical potential. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model.
• Score: 5.691318972818067
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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