AI 中文总结
该研究提出关联静态量子几何等的Floquet投影算符量子几何理论，用以表征受驱动手征对称可积自旋链的实空间量子态呼吸，为周期性驱动晶格系统微运动动力学研究提供支撑。
AI 中文摘要
对空间周期性量子系统进行周期性驱动会产生静态晶体中不存在的能带结构。我们提出一种量子几何理论，以同等地位表征频闪时刻及微运动过程中的Floquet-Bloch态。该框架基于随时间演化的Floquet投影算符构建，其关联了静态量子几何、微运动算符几何与Floquet拓扑。为阐释该形式体系，我们引入Floquet投影算符量子度量，并用其表征受手征对称可积自旋链中局域态的实空间呼吸效应。在布里渊区积分的Floquet投影算符量子度量，可捕捉微运动期间的振荡方差，且在对称性选定时刻，其下方由Floquet拓扑不变量界定。我们还描述了Floquet投影算符几何如何支撑对周期性驱动晶格系统中微运动动力学的系统性研究。
英文摘要
Periodic driving of spatially periodic quantum systems generates band structures that are absent in static crystals. We present a quantum geometric theory to characterize the Floquet-Bloch states at stroboscopic times and during micromotion on equal footing. Our framework builds upon time-evolved Floquet projectors that connect static quantum geometry, micromotion-operator geometry, and Floquet topology. To illustrate the formalism, we introduce the Floquet-projector quantum metric, which we employ to characterize the real-space breathing of localized states in a driven chiral-symmetric integrable spin chain. The Floquet-projector quantum metric, integrated over the Brillouin zone, captures the oscillatory variance during micromotion and, at symmetry-selected times, is bounded below by Floquet topological invariants. We further describe how the Floquet projector geometry enables a systematic investigation of micromotion dynamics in periodically driven lattice systems.
Comments8 pages, 3 figures
