Quenching a quantum system involves three basic ingredients: the initial phase, the postquench target phase, and quantum dynamics, which may carry the information of the former two. Here we propose a dynamical theory, based on an interaction quench, to characterize both the equilibrium symmetry-breaking order and topological phases by nonequilibrium correlated quantum dynamics. We illustrate the theory with the Haldane-Hubbard model, which is quenched from an initial correlated magnetic phase to a topologically nontrivial regime. We show that the quench dynamics exhibit profound universal behaviors on the so-called band-inversion surfaces (BISs), from which both the topological phase in the weakly interacting regime and the correlated magnetic phase in the strongly interacting regime can be extracted. In particular, the topology is characterized by dynamical topological patterns emerging on BISs, which are robust against interaction-induced dephasing and heating; the symmetry-breaking order can be read out from a universal dynamical scaling behavior, which is valid beyond the mean-field theory. This work uncovers the first paradigm of nonequilibrium characterization of equilibrium symmetry-breaking and topological phases.

中文翻译：

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平衡相关量子相的非平衡表征

淬火量子系统涉及三个基本成分：初始阶段、淬火后目标阶段和量子动力学，量子动力学可能携带前两者的信息。在这里，我们提出了一种基于相互作用猝灭的动力学理论，通过非平衡相关量子动力学来表征平衡对称破坏顺序和拓扑相。我们用 Haldane-Hubbard 模型说明了该理论，该模型从初始相关磁相淬灭到拓扑非平凡状态。我们表明，淬火动力学在所谓的能带反转表面 (BIS) 上表现出深刻的普遍行为，从中可以提取弱相互作用区域中的拓扑相和强相互作用区域中的相关磁相。特别是，该拓扑的特点是在 BIS 上出现了动态拓扑模式，这些模式对相互作用引起的移相和加热具有鲁棒性；对称破缺阶数可以从一个普遍的动态标度行为中读出，这在平均场理论之外是有效的。这项工作揭示了平衡对称破坏和拓扑相的非平衡表征的第一个范式。