High-order perturbation theory for correlated Boson systems

过去几年见证了涉及量子光学和凝聚态物理的深远发展：现在超冷量子气体正在实现具有范例意义的多体系统。这可能最终开启了利用这些可控的实验室系统作为尚未解决的凝聚态问题的量子模拟器的可能性，就像费曼最初提出的那样。为了将这一设想变为现实，需要精确的理论参考数据来衡量实验测量。为此，我们的团队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低温玻色子的精确零度相图，并计算相关函数。在本项目中，这种方法将被完善并推动到数值可行性的极限，然后应用于各种实验兴趣设置。

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.