Many-body quantum dynamics slows down at low density
Xiao Chen, Yingfei Gu, Andrew Lucas
SciPost Phys. 9, 071 (2020) · published 12 November 2020
- doi: 10.21468/SciPostPhys.9.5.071
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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.
Cited by 25
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Xiao Chen,
- 2 Yingfei Gu,
- 3 Andrew Lucas