High-order perturbation theory for correlated Boson systems

在过去的几年里，量子光学和凝聚态物理学都取得了深远的发展：超冷量子气体正在实现重要的多体系统。这可能最终打开了使用这些可控性良好的实验室系统作为量子模拟器来解决尚未解决的凝聚态问题的可能性，就像费曼最初提出的那样。为了将这一愿景变为现实，需要精确的理论参考数据，以进行实验测量。为此，我们的小组已经开发了一种基于数值执行的高阶微扰理论的方法，该方法允许人们获得光学晶格中超玻色子的精确零温度相图，并计算相关的相关函数。在本项目中，这种方法将被改进并推到数值可行性的极限，然后应用于各种实验感兴趣的环境。

The last few years have witnessed a far-reaching development involving both quantum optics and condensed-matter physics: Paradigmatically important many-body systems are now being realized by ultracold quantum gases. This might eventually open up the possibility to employ these well-controllable laboratory systems as quantum simulators for still unsolved condensed-matter problems, in the sense originally suggested by Feynman. In order to turn this vision into reality, precise theoretical reference data are needed against which experimental measurements can be gauged. To this end, our group has developed an approach based on numerically executed high-order perturbation theory, which allows one to obtain accurate zero-temperature phase diagrams for ultrald Bosons in optical lattices, and to compute the relevant correlation functions. Within the present project, this approach shall be refined and pushed to the limit of numerical feasibility, and then be applied to various settings of experimental interest.