复平面上的微扰理论：例外点及其寻找
Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
摘要：
我们探讨量子化学在复平面的非厄米扩展及其与微扰论的联系。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，称为例外点。在介绍了复平面上的非厄米量子化学的基本概念，包括平均场Hartree-Fock近似和Rayleigh-Schrödinger微扰理论之后，我们提供了对奇点物理学进行的各种研究活动的历史概述。特别是，我们强调开创性的工作，在穆勒-Plesset微扰理论，其与量子相变的微扰系列的收敛行为。我们还讨论了几个remation技术（如Padé和二次逼近），可以提高整体精度的Møller-Plesset摄动级数在收敛和发散的情况下。每一个这些点都说明了使用哈伯德二聚体在半填充，这被证明是一个通用的模型，用于理解的微妙的解析连续微扰理论在复杂的平面。
英文摘要：
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--Schrödinger 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 Møller--Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Padé and quadratic approximants) that can improve the overall accuracy of the Møller--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.
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