Floquet热化发作
Onset of Floquet Thermalisation
摘要：
在存在相互作用的情况下，一个封闭的、均匀的（无无序的）多体系统被认为在受到周期性驱动时一般会加热到“无限温度”的系综：根据支撑统计力学的遍历性假设的精神，这是因为没有能量或其他守恒定律阻止这一点。在这里，我们提出了一个相互作用的伊辛链驱动的时间依赖性的强度，这样的加热开始只有低于阈值的驱动幅度，高于该系统表现出非遍历行为的字段。开始出现在{ \it强，但不快}驾驶时。这特别使它超出了高频扩展的范围。起始位置的变化，但它是鲁棒存在的，跨越广泛的变化的模型哈密顿量，如驱动频率和协议，以及初始状态。在Floquet谱中的非遍历态部分，虽然是次显性的，但具有有限的熵。我们发现，磁化作为一个{ \it紧急}守恒量支撑的冻结，事实上，冻结效果是很容易观察到的，因为最初的磁化状态保持部分冻结{ \it无限时间}。这一结果与经典动力系统的Kolmogorov-Arnold-Moser定理有着家族相似之处，可能是将Floquet工程扩展到相互作用领域的一个有价值的成分。
英文摘要：
In presence of interactions, a closed, homogeneous (disorder-free) many-body system is believed to generically heat up to an `infinite temperature' ensemble when subjected to a periodic drive: in the spirit of the ergodicity hypothesis underpinning statistical mechanics, this happens as no energy or other conservation law prevents this. Here we present an interacting Ising chain driven by a field of time-dependent strength, where such heating onsets only below a threshold value of the drive amplitude, above which the system exhibits non-ergodic behaviour. The onset appears at {\it strong, but not fast} driving. This in particular puts it beyond the scope of high-frequency expansions. The onset location shifts, but it is robustly present, across wide variations of the model Hamiltonian such as driving frequency and protocol, as well as the initial state. The portion of nonergodic states in the Floquet spectrum, while thermodynamically subdominant, has a finite entropy. We find that the magnetisation as an {\it emergent} conserved quantity underpinning the freezing; indeed the freezing effect is readily observed, as initially magnetised states remain partially frozen {\it up to infinite time}. This result, which bears a family resemblance to the Kolmogorov-Arnold-Moser theorem for classical dynamical systems, could be a valuable ingredient for extending Floquet engineering to the interacting realm.
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