论文标题
在绝热限制中定期驱动系统中的基于时间的Chern号
A time-based Chern number in periodically-driven systems in the adiabatic limit
论文作者
论文摘要
为了定义驱动系统的拓扑结构，最近的作品提出了合成维度，以此来揭示拓扑不变的基础参数空间。将时间用作合成维度以及动量维度，可访问合成2D Chern号。但是，尚不清楚合成2D Chern号与Chern数字如何相关，该数字是根据随时间演变而来的参数变量定义的。在这里，我们表明，在绝热限制的定期驱动系统中，合成2D Chern号是由参数变量定义的Chern号的倍数。因此，可以通过参数变量在其自身空间中演变的合成2D Chern编号进行设计。我们通过研究两个1D紧密结合模型，一个三站链模型和两个1D 1-1-SLIDED链模型中的无泵来证明我们的主张是合理的。本发现可以扩展到更高的维度和其他定期驱动的配置。
To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension, gives access to a synthetic 2D Chern number. It is, however, still unclear how the synthetic 2D Chern number is related to the Chern number that is defined from a parametric variable that evolves with time. Here we show that in periodically driven systems in the adiabatic limit, the synthetic 2D Chern number is a multiple of the Chern number defined from the parametric variable. The synthetic 2D Chern number can thus be engineered via how the parametric variable evolves in its own space. We justify our claims by investigating Thouless pumping in two 1D tight-binding models, a three-site chain model and a two-1D-sliding-chains model. The present findings could be extended to higher dimensions and other periodically driven configurations.
