标题： 二维空间对称性分类在非厄米哈密顿量中的点隙AZ和AZ$^†$类别 显示英文标题

标题： Classifying Order-Two Spatial Symmetries in Non-Hermitian Hamiltonians: Point-gapped AZ and AZ$^†$ Classes

摘要： 晶体拓扑绝缘体和超导体一直是凝聚态物理领域的一个重要课题。 这些系统遵守某些晶体（空间）对称性，这些对称性取决于晶格的几何结构。 空间对称性的存在可能导致十重Altland Zirnbauer类的分类发生变化，从而产生新的受对称性保护的拓扑相。 如果厄米性约束被破坏，分类将扩展为38重。 在本文中，遵循厄米系统中的程序，我们对16种非厄米拓扑类中的点隙非厄米系统的所有可能的二阶空间对称性进行分类。 这16类由AZ和AZ^$\dag$类表示。 我们表明，类似于厄米情况，空间对称性也会导致AZ和AZ^$\dag$类的分类发生变化。 还存在仅属于点隙非厄米哈密顿量的新奇对称性保护的拓扑相。 基于我们的分类，也给出了玩具模型。 显示英文摘要

摘要： Crystalline topological insulators and superconductors have been a prominent topic in the field of condensed matter physics. These systems obey certain crystalline (spatial) symmetries that depend on the geometry of the lattice. The presence of spatial symmetries can lead to shift in the classification of ten fold Altland Zirnbauer class, given rise to new symmetry protected topological phases. If the constraint of Hermiticity is broken, the classification expand into 38 fold. In this paper, following procedures in Hermitian systems, we classify all possible types of order-two spatial symmetries for point gapped non Hermitian systems within 16 out of 38 non Hermitian topological classes. These 16 classes are denoted by AZ and AZ^$\dag$ classes. We show that, similar to the Hermitian case, spatial symmetries will also lead to a shift in the classification of AZ and AZ^$\dag$ classes. There also exist novel symmetry protected topological phases exclusive to point gapped non Hermitian Hamiltonians. Toy models are also given based on our classifications.