论文标题
与$ u（1）$对称性在二维的互动floquet阶段的分类
Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions
论文作者
论文摘要
我们在两个空间维度中与$ u（1）$对称性相互作用的玻色子和费米子的浮标阶段进行了完整的分类。根据我们的分类，这些浮雕阶段与有理功能之间有一对一的对应关系$π（z）= a（z）/b（z）$，其中$ a（z）$和$ b（z）$是多项式的某些条件，$ z $是一个正式参数。 The physical meaning of $π(z)$ involves the stroboscopic edge dynamics of the corresponding Floquet system: in the case of bosonic systems, $π(z) = \frac{p}{q} \cdot \tildeπ(z)$ where $\frac{p}{q}$ is a rational number which characterizes the flow of quantum information at the edge during each driving period, and $ \tildeπ（z）$是一个合理的函数，它表征了$ u（1）$电荷在边缘的流量。在费米子情况下存在类似的分解。我们还表明，$ \tildeπ（z）$与在特定几何形状中流动的时间平均$ u（1）$当前直接相关。此$ U（1）$电流是对先前对非相互作用的费米子浮球相的研究中发现的量化电流和量化磁化密度的概括。
We derive a complete classification of Floquet phases of interacting bosons and fermions with $U(1)$ symmetry in two spatial dimensions. According to our classification, there is a one-to-one correspondence between these Floquet phases and rational functions $π(z) = a(z)/b(z)$ where $a(z)$ and $b(z)$ are polynomials obeying certain conditions and $z$ is a formal parameter. The physical meaning of $π(z)$ involves the stroboscopic edge dynamics of the corresponding Floquet system: in the case of bosonic systems, $π(z) = \frac{p}{q} \cdot \tildeπ(z)$ where $\frac{p}{q}$ is a rational number which characterizes the flow of quantum information at the edge during each driving period, and $\tildeπ(z)$ is a rational function which characterizes the flow of $U(1)$ charge at the edge. A similar decomposition exists in the fermionic case. We also show that $\tildeπ(z)$ is directly related to the time-averaged $U(1)$ current that flows in a particular geometry. This $U(1)$ current is a generalization of the quantized current and quantized magnetization density found in previous studies of non-interacting fermionic Floquet phases.
