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Topological characterization of periodically driven quantum systems

机译:周期性驱动量子系统的拓扑表征

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Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two-dimensional hexagonal lattice tight-binding model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.
机译:物理系统的拓扑属性可以导致对微观细节不敏感的鲁棒行为。这种拓扑健壮的现象不仅限于静态系统,还可以出现在驱动量子系统中。在本文中,我们证明了周期驱动系统的Floquet算子可以划分为拓扑上不同的(同伦)类,并根据Floquet算子的频谱对该分类进行简单的物理解释。使用此图片,我们可以直观了解量化绝热泵送的众所周知的现象。 Floquet运算符属于琐碎类的系统模拟由与时间无关的哈密顿量生成的动力学,可以根据为静态系统开发的方案对它们进行拓扑分类。我们通过一个周期性驱动的二维六边形晶格紧密绑定模型的示例展示了这些原理,该模型显示了几个拓扑阶段。值得注意的是,即使大部分拓扑结构都很琐碎,这些阶段之一仍支持手性边缘模式。

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