论文标题
定期驱动的系统中的非热散装对应关系
Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
论文作者
论文摘要
连接大量拓扑结构和边缘状态的宽大对应关系是拓扑阶段的基本原理。然而，在一般的非铁族系统中，散装的对应关系被分解。在本文中，我们构建了具有定期驾驶的一维非su-schrieffer-Heeger模型，该模型表现出非富甲状性皮肤效应：所有特征状态都位于系统边界，无论是散装状态还是零状态和$π$模式。为了捕获拓扑特性，非Bloch绕组数是由基于广义的布里鲁因区的非Bloch周期演化算子定义的。此外，还建立了非荷马式散装对应关系：非Bloch绕组数字（$ W_ {0，π} $）用准固态来表征边缘状态$ε= 0，π$。在我们的非热系统中，一种新颖的现象可能会出现，即使浮球频带是拓扑琐事，零非BLOCH频带不变性也可以出现，该现象也可以出现，而非Bloch频带不变，该循环是根据非Blbloch有效的汉密尔顿人而定义的。我们还表明，非Bloch绕组数字（$ w_ {0，π} $）与非Bloch频段不变（$ \ Mathcal {w} $）之间的关系：$ \ Mathcal {w} = w_ {0} - w_π$。
Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits non-Hermitian skin effect: all the eigenstates are localized at the boundary of the systems, whether the bulk states or the zero and the $π$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers ($W_{0,π}$) characterize the edge states with quasienergies $ε=0, π$. In our non-Hermitian system, a novel phenomenon can emerge that the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch band invariant, which is defined in terms of the non-Bloch effective Hamiltonian. We also show that the relation between the non-Bloch winding numbers ($W_{0,π}$) and the non-Bloch band invariant ($\mathcal{W}$): $\mathcal{W}= W_{0}- W_π$.
