We consider a clean quantum system subject to strong periodic driving. The existence of a dominant energy scale, $h_D^x$, can generate considerable structure in an effective description of a system that, in the absence of the drive, is nonintegrable and interacting, and does not host localization. In particular, we uncover points of freezing in the space of drive parameters (frequency and amplitude). At those points, the dynamics is severely constrained due to the emergence of an almost exact, local conserved quantity, which scars the entire Floquet spectrum by preventing the system from heating up ergodically, starting from any generic state, even though it delocalizes over an appropriate subspace. At large drive frequencies, where a naïve Magnus expansion would predict a vanishing effective (average) drive, we devise instead a strong-drive Magnus expansion in a moving frame. There, the emergent conservation law is reflected in the appearance of the “integrability” of an effective Hamiltonian. These results hold for a wide variety of Hamiltonians, including the Ising model in a transverse field in any dimension and for any form of Ising interaction. The phenomenon is also shown to be robust in the presence of two-body Heisenberg interactions with any arbitrary choice of couplings. Furthermore, we construct a real-time perturbation theory that captures resonance phenomena where the conservation breaks down, giving way to unbounded heating. This approach opens a window on the low-frequency regime where the Magnus expansion fails.

中文翻译：

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强力驱动的浮球物质中的动态冻结和疤痕点：共振与新兴的守恒律

我们认为干净的量子系统会受到强烈的周期性驱动。存在主导的能量尺度，$H_d^X$可以在系统的有效描述中生成相当大的结构，该系统在没有驱动器的情况下是不可集成和交互的，并且不会托管本地化。特别是，我们发现了驱动参数（频率和幅度）空间中的冻结点。在这些时候，由于几乎精确的局部守恒量的出现，动力学受到了严重的限制，这吓到了整个人。通过阻止系统从任何一般状态开始遍历整个系统而升温，即使它在适当的子空间上未定位，也可以通过它来确定浮动频谱。在较大的驱动频率下，如果幼稚的Magnus扩展会预测有效（平均）驱动消失，我们会在移动框架中设计一个强驱动的Magnus扩展。在那里，有效的哈密顿量的“可积性”的出现反映了涌现的守恒定律。这些结果适用于各种各样的哈密顿量，包括任何尺寸的横向场中的伊辛模型以及任何形式的伊辛相互作用。该现象在具有任意选择的耦合的两体海森堡相互作用的情况下也显示出很强的鲁棒性。此外，我们构建了一个实时扰动理论，该理论捕获了共振现象，在该现象中守恒被破坏了，让位于无限加热。这种方法为Magnus扩展失败的低频状态打开了一个窗口。