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DOE OSTI · 1712538

Many-body quantum dynamics slows down at low density

Chen, Xiao·Gu, Yingfei·Lucas, Andrew
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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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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

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Chen, Xiao, Gu, Yingfei, Lucas, Andrew. 2020-11-12. Many-body quantum dynamics slows down at low density. https://doi.org/10.21468/scipostphys.9.5.071

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