零温有限系统的图解蒙特卡洛方法
Diagrammatic Monte Carlo for Finite Systems at Zero Temperature
AI总结：
本文提出适用于零温自束缚离散能级系统的图解蒙特卡洛算法，通过采样费曼图拓扑空间纳入高阶虚激发，并在 Richardson 模型中验证其潜力。
摘要：
高阶虚激发在中能核反应的微观模型中发挥着重要作用。然而，其复杂度的阶乘式增长阻碍了将它们一致地纳入从头算多体计算。对于有限温度下的无限系统，可以利用图解蒙特卡洛技术对整个费曼图级数进行重求和，从而克服这些缺陷。我们提出了一种图解蒙特卡洛算法，可应用于零温下具有离散能级的自束缚系统，并通过核配对的 Richardson 模型展示了其潜力。我们表明，对图的拓扑空间进行采样，能够纳入核物理与量子化学中最先进近似所忽略的高阶激发。我们认为，对图解空间进行采样可以弥合核物理中结构与反应的微观理解之间长期存在的鸿沟。
英文摘要：
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body calculations. For infinite systems at finite temperature, such drawbacks can be overcome using diagrammatic Monte Carlo techniques to resum entire series of Feynman diagrams. We present a diagrammatic Monte Carlo algorithm that can be applied to self-bound systems with discrete energy levels at zero temperature, and demonstrate its potential for the Richardson model of nuclear pairing. We show that sampling the topological space of diagrams allows the inclusion of high-order excitations that are neglected in state-of-the-art approximations used in nuclear physics and quantum chemistry. We propose that sampling the diagrammatic space can overcome the long-standing gap between our microscopic understanding of structure and reactions in nuclear physics.
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