qwz模型的边缘态 如何做出它的边缘态呢？ 直接的想法就是进行一个完全的模拟， N_x,N_y 取有限值，求解它的能带看是否具有edge state，这种想法原则上是OK的，可以去做，但问题在于如果两边都没有平移对称性的话，那么这个系统就没有一个好的量子数来lable能级 ...

Asboth那本short course对于 拓扑绝缘体 的dimension extension的一个绝佳例子就是用Rice-Mele model 到 Qi-Wu-Zhang model 的过渡来展示的，书中的表6.1对此讲述的很明确： 体 哈密顿 可以用三个Pauli矩阵写出来，因此体色散是有 解析解 的： 能带在 u=\pm2,0 时存在BZ高对称点的 Dirac\,cone ： 复现： 对于体拓扑的分析采用类似winding number的graphical way： 拓扑情形的半无限大体系： 对于边界处施加次紧邻扰动和在位能扰动： 书中红/蓝色高亮能带代表右图的红/ …

QWZ model 的图像，(N,M)=(20,20) 我们能看出来能量的分布（因为这个与混合边条在 E 轴上的投影类似）和边界态，但是得到的信息还是比较少，比如我们想研究上面模型中能隙中的 狄拉克点 的性质，就是毫无办法（你能看得出来有个狄拉克点吗？

A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions, arXiv:1509.02295v1 (9.9. 2015)

Our aim in this paper is to explain the appearance of chiral edge-modes in the nontrivial phase of a 2D Chern insulator, namely the Qi-Wu-Zhang (QWZ) model [5], and develop a method for studying the topological phase transition in this model in terms of the edge-modes alone.

2016年2月23日 · To illustrate the concepts of Chern insulators, we will use a toy model introduced by Qi, Wu and Zhang [24], which we call the QWZ model. This model is also important because it forms the basic building block of the Bernevig-Hughes-Zhang model for the Quantum Spin Hall Effect (Chap. 8), and thus it is also sometimes called “half BHZ”.

2023年1月17日 · Based on the optical Raman lattice technique, we experimentally realize the Qi-Wu-Zhang model for the quantum anomalous Hall phase in ultracold fermions with two-dimensional (2D) spin-orbit (SO) coupling.

Our aim in this paper is to explain the appearance of chiral edge-modes in the nontrivial phase of a 2D Chern insulator, namely the Qi-Wu-Zhang(QWZ) model [5], and develop a method for studying the topological phase transition in this model in terms of the edge-modes alone.

• Foundation of QWZ model is the adiabatic smooth pump sequence of the Rice-Mele model • Transformed from a 1D time dependant Hamiltonian to a 2D in bulk momentum space • Cyclic parameter in a continuous ensemble is Promoted to a momentum parameter Hˆ (k,t) ! Hˆ (k x,ky) 3

阐述了陈绝缘体二维模型（即 Qi-Wu-Zhang (QWZ) 模型）中拓扑相变的开始，特别强调了手征边缘模式的出现。 通过使用称为维度扩展的技术分析一维电荷泵等效模型中的边缘状态动态来研究边缘模式。