We explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including the mean-field Hartree–Fock approximation and Rayleigh–Schrdinger perturbation theory, we provide a historical overview of the various research activities that have been performed on the physics of singularities. In particular, we highlight seminal work on the convergence behaviour of perturbative series obtained within Mller–Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Pad and quadratic approximants) that can improve the overall accuracy of the Mller–Plesset perturbative series in both convergent and divergent cases. Each of these points is illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane.

我们探索了复平面中量子化学的非厄米扩展及其与微扰理论的联系。我们观察到量子系统的物理学与复值能量奇点的位置密切相关，称为异常点。在介绍了复平面中非厄米量子化学的基本概念，包括平均场 Hartree-Fock 近似和 Rayleigh-Schrdinger 微扰理论之后，我们提供了对物理学的各种研究活动的历史概述。奇点。我们特别强调了在 Mller-Plesset 微扰理论中获得的微扰级数收敛行为的开创性工作，及其与量子相变的联系。我们还讨论了几种可以提高 Mller-Plesset 微扰级数在收敛和发散情况下的整体精度的求和技术（例如 Pad 和二次近似）。这些点中的每一个都使用半填充时的哈伯德二聚体来说明，这被证明是一种通用模型，用于理解复平面中分析连续微扰理论的微妙之处。