论文标题
将约旦分解应用于具有光谱分离的较低态状态的非热晶格模型
Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
论文作者
论文摘要
在分析非热晶格系统时，必须用约旦分解来代替用于遗传系统分析的标准本本特征分解。这种方法使我们能够确定大型有限大小的晶格系统的正确数量的左右特征状态，并为计算系统的谐振激发构成完整的基础。具体而言，我们得出了将Jordan分解应用于具有光谱均匀状态的系统的程序。我们使用具有零能量角状态的非热二极管绝缘子作为大型系统的一个示例，其维度可以大幅度降低，以得出描述这种本地化状态的低维度“有缺陷的”汉密尔顿。使用约旦分解方法来解释系统附近能量的谐振响应的反直觉和非本地性能。根据角状态的激发属性，我们将非血压四极性绝缘因子分为三类：琐碎，近乎近海和非本地。
When analyzing non-Hermitian lattice systems, the standard eigenmode decomposition utilized for the analysis of Hermitian systems must be replaced by Jordan decomposition. This approach enables us to identify the correct number of the left and right eigenstates of a large finite-sized lattice system, and to form a complete basis for calculating the resonant excitation of the system. Specifically, we derive the procedure for applying Jordan decomposition to a system with spectrally-isolated states. We use a non-Hermitian quadrupole insulator with zero-energy corner states as an example of a large system whose dimensionality can be drastically reduced to derive a low-dimensional "defective" Hamiltonian describing such localized states. Counter-intuitive and non-local properties of the resonant response of the system near zero energy are explained using the Jordan decomposition approach. Depending on the excitation properties of the corner states, we classify our non-Hermitian quadrupolar insulator into three categories: trivial, near-Hermitian, and non-local.
