本文研究了一维锯齿晶格中自旋轨道耦合与Zeeman场驱动的双组分费米气体的拓扑性质。我们理论计算了系统的能谱,利用矩阵乘积态(MPS)数值研究了多个物理量(系统的边界态、冯诺依曼熵、纠缠谱和激发能隙),并据此分析了系统的拓扑性质。发现在填充因子为半填充时,边界态的存在可以用来表征系统的拓扑性。而填充因子为1/4(或3/4)时,虽然系统存在边界态,但该系统并不具备一般拓扑态的其他特征,该类边界态不能用于表征拓扑态。

In this paper,the topological properties of two-component Fermi gas driven by spin-orbit coupling and Zeeman field in a one-dimensional sawtooth lattice were studied.The energy spectrum of system was calculated theoretically,and some quantities such as the edge state,von Neumann entropy,entanglement spectrum and excitation energy gap were computed numerically by matrix product state (MPS).The topological properties of the system were analyzed based on these results.It was found that the presence of edge states can be used to demonstrate the topology of the system at half filling.With the 1/4 (or 3/4) fill factor although the system has a single edge state,it does not possess other features of the general topological state.Therefore,such edge state cannot characterize the topological state.