中文摘要：

在这篇文章，我们在二维的强烈相关的费米子系统在量阶段转变上考察我们的最近的工作。我们由用细胞的动态吝啬地的理论(CDMFT ) 和连续时间的量蒙特卡罗算法的联合计算状态，两倍占有，和费密表面进化的密度讨论这些系统的 metalinsulator 转变性质。而且，我们由定义磁性的顺序参数探索每个状态的磁性。包括 antiferromagnetic 金属，顺磁的金属， Kondo 金属，和铁磁性的绝缘体，有许多吸引人的量状态的富有的阶段图被作出对有利的裁决有强烈相关的费米子的二维的格子。我们相信我们的结果将导致真实材料的性质的更好的理解。

英文摘要：

In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal insulator transition properties of these systems by calculating the density of states, double occupancy, and Fermi surface evolution using a com- bination of the cellular dynamical mean-field theory （CDMFT） and the continuous-time quantum Monte Carlo algorithm. Furthermore, we explore the magnetic properties of each state by defining magnetic order parameters. Rich phase diagrams with many intriguing quantum states, including antiferromagnetic metal, paramagnetic metal, Kondo metal, and ferromagnetic insulator, were found for the two-dimensional lattices with strongly correlated fermions. We believe that our results would lead to a better understanding of the properties of real materials.