Topological classification of non-Hermitian systems with reflection symmetry
Topological classification of non-Hermitian systems with reflection symmetry
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DOI：
10.1103/physrevb.99.125103
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发表时间：
2018-12
影响因子：
3.7
通讯作者：
Chun-hui Liu;Hui Jiang;Shu Chen
中科院分区：
文献类型：
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作者：
Chun-hui Liu;Hui Jiang;Shu Chen
我们分类拓扑阶段的非厄米系统在Altland Zirnbauer类与额外的反射对称性在所有维度。通过将非厄米系统映射为具有强制手征对称性的厄米哈密顿量，我们的拓扑分类等价于同时具有手征对称性和反射对称性的厄米系统的分类，从而有效地改变了分类空间，并移动了拓扑相的周期表.根据我们的分类表，我们提供了具体的例子，所有的拓扑非平凡的非厄米特类在一个维度上，也明确给出了每个非平凡的例子的拓扑不变量。我们的结果表明，存在两种拓扑不变量，它们要么由缠绕数组成，要么由${\mathbb{Z}}_{2}$数组成.通过研究开边界条件下相应的格点模型，揭示了以缠绕数为特征的一维拓扑非厄米特系统存在体-边对应，但在我们研究的${\mathbb {Z}}{2}$型模型中，没有观察到拓扑数为${\mathbb {Z}{2}$时的体-边对应.
We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced chiral symmetry, our topological classification is thus equivalent to classifying Hermitian systems with both chiral and reflection symmetries, which effectively change the classifying space and shift the periodical table of topological phases. According to our classification tables, we provide concrete examples for all topologically nontrivial non-Hermitian classes in one dimension and also give explicitly the topological invariant for each nontrivial example. Our results show that there exist two kinds of topological invariants composed of either winding numbers or ${\mathbb{Z}}_{2}$ numbers. By studying the corresponding lattice models under the open boundary condition, we unveil the existence of bulk-edge correspondence for the one-dimensional topological non-Hermitian systems characterized by winding numbers, however we did not observe the bulk-edge correspondence for the ${\mathbb{Z}}_{2}$ topological number in our studied ${\mathbb{Z}}_{2}$-type model.