论文标题
复杂平面中的摄动理论：特殊点和在哪里找到它们
Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
论文作者
论文摘要
我们探讨了复杂平面中量子化学的非热延伸，并与其与扰动理论的联系。我们观察到，量子系统的物理学与复杂值能量奇异性（称为特殊点）的位置密切相关。在介绍了复杂平面中非血液量子化学的基本概念之后，包括平均场hartree-频率近似和雷利 - 瑞格丁·扰动理论，我们提供了有关在奇异物理学上进行的各种研究活动的历史概述。特别是，我们重点介绍了Møller-插动理论中获得的扰动序列的收敛行为及其与量子相变的联系。我们还讨论了几种可以提高Møller的总体准确性的重新召集技术（例如PADé和二次近似值） - 在收敛性和发散病例中，Plesset扰动系列。使用Half填充的Hubbard Dimer说明了这些点中的每一个，这被证明是一个多功能模型，用于理解复杂平面中分析性扰动理论的微妙之处。
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.
