How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-$1/2$ particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.

中文翻译：

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陷阱离子量子模拟器中的多体相移

封闭的相互作用量子多体系统如何随时间松弛和消相是热力学和统计物理学的基本问题。在这封信中，我们分析并观察了用俘获离子量子模拟器实现的可调谐长程相互作用横向场伊辛哈密顿量的量子猝灭后的持续时间波动。我们测量了自旋有限元系统的平均磁化强度的时间波动$\mathrm{1个}/2$粒子。我们在一个系统的属性与具有全局自旋-自旋耦合的可积分哈密顿量密切相关的系统中进行了实验，这可以对长期不可积分动力学进行分析预测。时间波动的解析表达式预测随着系统规模的增大，时间波动的指数抑制。我们的测量数据与预测多相移相状态的理论相符。