论文标题
实现在对称存在下任何顺序的特殊点
Realizing exceptional points of any order in the presence of symmetry
论文作者
论文摘要
特殊点〜（EPS）在特征向量融合的非热矩阵的频谱中显示为归化。通常，如果施加$ 2（n-1）$，则可能会找到订单$ n $的EP。我们的结果表明，这些约束可以用非省矩阵的决定因素和痕迹表示。我们的发现进一步表明，在存在统一和反对对称性的情况下，约束总数可能会减少。此外，我们为EPS的低能分散得出一般结论。根据我们的计算，我们表明，在奇数上，sublattice或伪手续的对称性的存在强制执行$ n $ th订单EPS以分散$（n-1）$ th root。对于两，三波段系统，我们明确地介绍了EPS在系统参数方面发生所需的约束，并根据其低能量分散关系对EP进行分类。
Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show that these constraints can be expressed in terms of the determinant and traces of the non-Hermitian matrix. Our findings further reveal that the total number of constraints may reduce in the presence of unitary and antiunitary symmetries. Additionally, we draw generic conclusions for the low-energy dispersion of the EPs. Based on our calculations, we show that in odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces $n$th order EPs to disperse with the $(n-1)$th root. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters and classify EPs based on their low-energy dispersion relations.
