论文标题
增强的特征向量灵敏度和sublattice-Memmore特殊点的代数分类
Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
论文作者
论文摘要
特殊点（EPS）是非热汉顿人的堕落，在该二元组中，特征值及其特征向量colesce colesce。他们的命令由约旦分解给出。在这里，我们专注于带有Sublattice对称性的费米子系统中产生的高阶EP，这限制了Hamitlonian的特征值以$ \ lbrace e，-e \ rbrace $成对出现。因此，幼稚的预测可能仅导致偶数EPS在零能量下。但是，我们表明奇数EP可以存在，并且根据我们如何接近退化点的方式，在其附近特征向量钙化的行为方面表现出增强的敏感性。奇数EPs可以理解为高价值和均值均衡EPS的混合物。这种异常行为与EPS的不规则拓扑相关，如所讨论的汉密尔顿人的子空间，这是约旦障碍的独特特征。可以通过观察到与目标特征向量的量子距离如何收敛到零来描述增强的特征向量灵敏度。为了捕获特征向量 - 钙化，我们提供了一种代数方法来描述这些EPS存在的条件。这是基于结果和判别因素的先前研究，并揭示了迄今未开发的高阶异常退化结构。
Exceptional points (EPs) are degeneracy of non-Hermitian Hamiltonians, at which the eigenvalues, along with their eigenvectors, coalesce. Their orders are given by the Jordan decomposition. Here, we focus on higher-order EPs arising in fermionic systems with a sublattice symmetry, which restricts the eigenvalues of the Hamitlonian to appear in pairs of $\lbrace E, -E\rbrace $. Thus, a naive prediction might lead to only even-order EPs at zero energy. However, we show that odd-order EPs can exist and exhibit enhanced sensitivity in the behaviour of eigenvector-coalescence in their neighbourhood, depending on how we approach the degenerate point. The odd-order EPs can be understood as a mixture of higher- and lower-valued even-order EPs. Such an anomalous behaviour is related to the irregular topology of the EPs as the subspace of the Hamiltonians in question, which is a unique feature of the Jordan blocks. The enhanced eigenvector sensitivity can be described by observing how the quantum distance to the target eigenvector converges to zero. In order to capture the eigenvector-coalescence, we provide an algebraic method to describe the conditions for the existence of these EPs. This complements previous studies based on resultants and discriminants, and unveils heretofore unexplored structures of higher-order exceptional degeneracy.
