论文标题
Hermitian拓扑起源于非赫米特辫子
Hermitian Topologies originating from non-Hermitian braidings
论文作者
论文摘要
即使在一个维度上，非热系统的复杂能带在动量空间中编织。在这里，我们透露，在一个统一Hermitian和Non-Hermitian系统的一般框架下，非热式编织是用手性对称性的Hermitian拓扑物理学的基础。特别是，我们得出了一种优雅的身份，该身份将编织的非铁带和零能环之间的链接数等同于一个维度的手性 - 对称拓扑阶段的拓扑不变。此外，我们发现了由临界点转化的一个异国情调的相变，该临界点转化了非铁质编织的不同结结构，这些结构未包含在传统的Hermitian拓扑相变理论中。然而，我们展示了Hermitian拓扑绝缘子的散装非铁质编织与边界零模式之间的巨大对应关系。最后，我们使用非武辫构建典型的拓扑阶段，可以通过人造晶体很容易实现。
The complex energy bands of non-Hermitian systems braid in momentum space even in one dimension. Here, we reveal that the non-Hermitian braiding underlies the Hermitian topological physics with chiral symmetry under a general framework that unifies Hermitian and non-Hermitian systems. Particularly, we derive an elegant identity that equates the linking number between the knots of braiding non-Hermitian bands and the zero-energy loop to the topological invariant of chiral-symmetric topological phases in one dimension. Moreover, we find an exotic class of phase transitions arising from the critical point transforming different knot structures of the non-Hermitian braiding, which are not included in the conventional Hermitian topological phase transition theory. Nevertheless, we show the bulk-boundary correspondence between the bulk non-Hermitian braiding and boundary zero-modes of the Hermitian topological insulators. Finally, we construct typical topological phases with non-Hermitian braidings, which can be readily realized by artificial crystals.
