论文标题
拓扑量子步行，带离散的时间网对称性
Topological Quantum Walk with Discrete Time-Glide Symmetry
论文作者
论文摘要
离散的量子步行是定期驱动的系统，具有离散的时间演变。与普通的Floquet系统相反，不存在微观汉密尔顿，并且一系列单一操作员直接给出了一个周期的时间演变。关于每个构成统一操作员作为离散的时间步，我们在量子步行中制定离散的时空对称性，并评估相应的对称性受保护的拓扑阶段。特别是，我们研究了这种形式主义的手性和/或时间网对称拓扑量子量。由于时间演变的离散性质，发现拓扑分类与传统的浮雕系统中的分类不同。作为一个具体的例子，我们研究了具有手性和时光对称性的二维量子步行，并确定受这些对称性保护的异常边缘状态。
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary operators. Regarding each constituent unitary operator as a discrete time step, we formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases. In particular, we study chiral and/or time-glide symmetric topological quantum walks in this formalism. Due to discrete nature of time evolution,the topological classification is found to be different from that in conventional Floquet systems. As a concrete example, we study a two-dimensional quantum walk having both chiral and time-glide symmetries, and identify the anomalous edge states protected by these symmetries.
