Topological quantum walk with discrete time-glide symmetry
Topological quantum walk with discrete time-glide symmetry
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DOI：
10.1103/physrevb.102.035418
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发表时间：
2020-04
影响因子：
3.7
通讯作者：
Ken Mochizuki;Takumi Bessho;M. Sato;H. Obuse
中科院分区：
文献类型：
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作者：
Ken Mochizuki;Takumi Bessho;M. Sato;H. Obuse
离散量子行走是具有离散时间演化的周期性驱动系统。与普通的Floquet系统不同，该系统不存在微观哈密顿量，一周期的时间演化直接由一系列酉算子给出。将每个构成么正算符看作一个离散的时间步长，建立了量子游动中的离散时空对称性，并计算了相应的对称性保护的拓扑相。特别地，我们在这种形式下研究了手征和/或时间滑动对称的拓扑量子游动。由于时间演化的离散性质，这种拓扑分类不同于传统的Floquet系统。作为一个具体的例子，我们研究了同时具有手征对称性和时间滑动对称性的二维量子行走，并识别了受这些对称性保护的反常边态。
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.