Action-based quantum Monte Carlo approach to fermion-boson lattice models

通过扩展连续时间量子蒙特卡罗方法，本项目旨在了解描述费米电荷载流子与玻色子自由度（如声子或磁振子）相互作用的模型中的基本效应。这里感兴趣的模型捕捉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。基于作用的路径积分公式的连续时间量子蒙特卡罗方法允许包括一般的，非局部的两粒子相互作用介导的玻色子。要解决的重要方面包括Peierls过渡，极化子的形成，电荷密度波秩序和超导性之间的竞争，在聚合物中的孤子激发，以及电子配对的自旋波动的作用。

By extending the continuous-time quantum Monte Carlo method, this project aims at understanding fundamental effects in models describing the interaction of fermionic charge carriers with bosonic degrees of freedom such as phonons or magnons. The models of interest here capture electronic correlations and quantum fluctuations, and pose a challenge even to state of the art numerical methods. The action-based path-integral formulation of the continuous-time quantum Monte Carlo method permits to include general, nonlocal two-particle interactions mediated by bosons. Important aspects to be addressed include the Peierls transition, polaron formation, the competition between charge-density-wave order and superconductivity, soliton excitations in polymers, and the role of spin fluctuations for electronic pairing.