We show how, given a non-Hermitian Hamiltonian $H$, we can generate new non-Hermitian operators sequentially, producing a virtually infinite chain of non-Hermitian Hamiltonians which are isospectral to $H$ and $H^{†}$ and whose eigenvectors we can easily deduce in an almost automatic way; no ingredients are necessary other than $H$ and its eigensystem. To set off the chain and keep it running, we use, for the first time in our knowledge, a series of maps all connected to different metric operators. We show how the procedure works in several physically relevant systems. In particular, we apply our method to various versions of the Hatano–Nelson model and to some PT-symmetric Hamiltonians.

我们展示给定非埃尔米特哈密顿量 $H$，我们可以依次生成新的非Hermitian算子，从而产生几乎无限的非Hermitian哈密顿量链 $H$ 和 $H^{†}$我们可以很容易地以几乎自动的方式推导出其特征向量；除了没有其他必要的成分$H$及其本征系统。为了启动链并使其保持运行，我们第一次了解到，使用了一系列都连接到不同度量运算符的地图。我们展示了该程序如何在几个物理相关的系统中工作。特别是，我们将我们的方法应用于Hatano-Nelson模型的各种版本以及某些PT对称哈密顿量。