论文标题
粒子数和角动量的投影：三轴Bogoliubov Quasiparticle状态的示例
Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
论文作者
论文摘要
许多旨在描述自我结合核或介镜电子系统的数量多体方法，利用了辅助波函数破坏了哈密顿量的一个或几个对称性，以包括与系统组成部分的几何布置相关的相关性。这种参考状态已经在基于有效的价空间汉密尔顿人或能量密度功能的自洽方法中已经使用了很长时间了，目前它们在新颖的AB-Initio方法的设计中也越来越受欢迎。然而，对自我结合的多体系统的完全量化处理需要通过投影对良好的量子数的多体波函数的投影来恢复损坏的对称性。这项工作的目标是三倍。首先，我们要从小组代表理论的基本原理开始，对投影方法的形式主义进行一般性介绍。其次，我们希望研究Bogoliubov Quasiparticle真空吸尘器的粒子数和角度投影的数值实现的形式和实际方面，尤其是以最小的计算成本获得准确的结果。第三，我们希望分析突破性状态在投影时的内在对称性的数值，计算和物理后果。
Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include correlations associated with the geometrical arrangement of the system's constituents. Such reference states have been used already for a long time within self-consistent methods that are either based on effective valence-space Hamiltonians or energy density functionals, and they are presently also gaining popularity in the design of novel ab-initio methods. A fully quantal treatment of a self-bound many-body system, however, requires the restoration of the broken symmetries through the projection of the many-body wave functions of interest onto good quantum numbers. The goal of this work is three-fold. First, we want to give a general presentation of the formalism of the projection method starting from the underlying principles of group representation theory. Second, we want to investigate formal and practical aspects of the numerical implementation of particle-number and angular-momentum projection of Bogoliubov quasiparticle vacua, in particular with regard of obtaining accurate results at minimal computational cost. Third, we want to analyze the numerical, computational and physical consequences of intrinsic symmetries of the symmetry-breaking states when projecting them.
