论文标题
多体量子动力学以低密度减速
Many-body quantum dynamics slows down at low density
论文作者
论文摘要
我们研究了具有全球U（1）保护法的量子多体系统，重点介绍了$ n $相互作用的费用与电荷保护的理论，或者$ n $相互作用的旋转具有总旋转的一个保守成分。我们通过适当正规的超时订购的相关功能来定义有限化学势的有效运算符尺寸。该密度依赖性操作员大小的生长速率随电荷密度而消失。因此，我们以给定密度的带电系统中的Lyapunov指数和蝴蝶速度获得了新的界限，该密度比任何Lieb-Robinson结合的参数强。我们认为，在带电的sachdev-ye-kitaev模型中，我们绑定对Lyapunov指数的密度依赖性已饱和。我们还研究了随机的自动机量子电路和布朗sachdev-ye-kitaev模型，每个模型对Lyapunov指数表现出不同的密度依赖性，并解释了差异。我们建议我们的结果是在有限温度下理解普朗克受限能量持有能力的动力学的卡通。
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.
