We develop a graphic approach for characterizing one-dimensional non-Hermitian topological phases. The eigenstates of energy bands are mapped to a graph on the torus, where a nontrivial topology exhibits as links. The topology of band touching exceptional points is a crucial aspect of a non-Hermitian system; the existence of exceptional point results in networks. We discuss the parity-time ( ##IMG## [http://ej.iop.org/images/2399-6528/4/9/095005/jpcoabb24cieqn1.gif] {${ \mathcal P }{ \mathcal T }$} ) symmetric two-band models. The pseudo-anti-Hermiticity protects the band topology, and the eigenstate graphs in the exact ##IMG## [http://ej.iop.org/images/2399-6528/4/9/095005/jpcoabb24cieqn2.gif] {${ \mathcal P }{ \mathcal T }$} -symmetric phase locate on the torus surface under the ##IMG## [http://ej.iop.org/images/2399-6528/4/9/095005/jpcoabb24cieqn3.gif] {${ \mathcal P }{ \mathcal T }$} symmetry protection. For the ...

中文翻译：

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可视化一维非埃尔米特拓扑阶段

我们开发了一种用于表征一维非Hermitian拓扑阶段的图形方法。能带的本征态被映射到圆环上的图，其中非平凡的拓扑表现为链接。频带接触例外点的拓扑结构是非Hermitian系统的关键方面。网络中存在例外点的结果。我们讨论奇偶时间（## IMG ## [http://ej.iop.org/images/2399-6528/4/9/095005/jpcoabb24cieqn1.gif] {$ {\ mathcal P} {\ mathcal T } $}）对称两频带模型。伪反赫米特性可保护频段拓扑和精确的## IMG ## [http://ej.iop.org/images/2399-6528/4/9/095005/jpcoabb24cieqn2.gif]中的本征图{$ {\ mathcal P} {\ mathcal T} $}-对称相位位于## IMG ## [http：//ej.iop。org / images / 2399-6528 / 4/9/095005 / jpcoabb24cieqn3.gif] {$ {\ mathcal P} {\ mathcal T} $}对称保护。为了 ...