论文标题
手性浮雕系统和量子步行在半个时期
Chiral Floquet systems and quantum walks at half period
论文作者
论文摘要
我们将手性对称性定期驱动的量子系统分类为一维晶格。驾驶过程是本地的，可以是连续的或可以及时离散的，并且我们假设相应的浮球操作员有间隙条件。该分析是根据统一操作员在半期（半步操作员）上进行的。我们根据五个整数索引对半步操作员的连接类别进行完整的分类。根据这些指数，可以决定是否可以从连续的哈密顿驾驶中获得半步操作员。半步操作员确定了两个Floquet操作员，分别以零或半个周期开始驾驶获得。这些被称为时间范围，是手性对称量子步行。相反，我们在哪些条件下显示了两次手性对称步道决定了一个常见的半步操作员。此外，我们阐明了半步操作员的分类与相应的量子步行之间的连接。在该理论中，我们证明了散装的通信，并表明第二个时间范围允许在$+1 $和$ -1 $的对称性受保护的边缘状态区分，这对于单个时间范围是不可能的。
We classify chiral symmetric periodically driven quantum systems on a one-dimensional lattice. The driving process is local, can be continuous or discrete in time, and we assume a gap condition for the corresponding Floquet operator. The analysis is in terms of the unitary operator at a half-period, the half-step operator. We give a complete classification of the connected classes of half-step operators in terms of five integer indices. On the basis of these indices it can be decided whether the half-step operator can be obtained from a continuous Hamiltonian driving, or not. The half-step operator determines two Floquet operators, obtained by starting the driving at zero or at half period, respectively. These are called timeframes and are chiral symmetric quantum walks. Conversely, we show under which conditions two chiral symmetric walks determine a common half-step operator. Moreover, we clarify the connection between the classification of half-step operators and the corresponding quantum walks. Within this theory we prove bulk-edge correspondence and show that a second timeframe allows to distinguish between symmetry protected edge states at $+1$ and $-1$ which is not possible for a single timeframe.
