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.
Slow growth of quantum magic in disorder-free Stark many-body localization
Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；School of Physics and Optoelectronics, Xiangtan University（湘潭大学物理与光电工程学院）
$\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence
研究了超弱耦合到环境中的$\mathcal{P}\mathcal{T}$对称量子系统。我们发现，这样的开放系统下的$\mathcal{P}\mathcal{T}$ -对称，纯退相和酉动力学的发展。描述演化的动力学映射，然后确定明确使用量子正则变换。此外，我们提供了一个解释为什么$\mathcal{P}\mathcal{T}$ -对称退相型相互作用导致\emph{critical slowing down of decoherence}。这种效应进一步用实验相关系统--在光学或微腔实验中容易实现的$\mathcal{P}\mathcal{T}$对称量子位\emph{e.g.}--来举例说明。
