Action-Based Quantum Monte Carlo Approach to Fermion-Boson Lattice Models

利用量子蒙特卡罗方法，本项目旨在理解描述费米子载流子（电子、空穴）与玻色子自由度（声子、磁振子）相互作用的模型中的基本效应。这里感兴趣的模型捕获了电子相关性和量子涨落，甚至对最先进的数值方法提出了挑战。尽管有一些必要的简化，但与实验中研究的实际化合物有密切的联系。需要解决的重要方面包括从金属态到绝缘态的佩尔斯跃迁，极化载流子的形成，电荷密度、波序和超导性之间的竞争，聚合物中的孤子激发，以及自旋涨落在电子配对中的作用。这项工作的核心将是强大的连续时间量子蒙特卡罗方法，它的一般基于作用的公式使我们能够研究各种各样的物理问题。

Using the quantum Monte Carlo method, this project aims at understanding fundamental effects in models describing the interaction of fermionic charge carriers (electrons, holes) with bosonic degrees of freedom (phonons, magnons). The models of interest here capture electronic correlations and quantum fluctuations, and pose a challenge even to state of the art numerical methods. Despite some necessary simplifications, there are close connections to real compounds studied in experiments. Important aspects to be addressed include the Peierls transition from a metallic to an insulating state, the formation of polaronic charge carriers, the competition between charge density wave order and superconductivity, soliton excitations in polymers, and the role of spin fluctuations for electronic pairing. At the heart of this work will be the powerful continuous-time quantum Monte Carlo method, whose general action-based formulation allows us to study a great variety of physical problems.