论文标题
多波段SSH模型中的绕组数和Zak阶段
Winding number and Zak phase in multi-band SSH models
论文作者
论文摘要
我们使用多波段SSH模型来演示用于计算正确的Zak相和绕组数的多波段系统的处方。我们通过将四波段SSH模型的最终绕组数与半无限链的边缘进行比较来验证我们的处方，我们通过求解运动方程来找到。然后，我们还通过解决具有各种位点的有限链的矩阵特征值问题来进行了广泛的比较与获得的数值结果。作为对我们的处方的双重检查，我们还确认了六波段SSH模型中的大量边缘对应。与通常的SSH模型相似，如果系统中违反了空间反转对称性，则与有限链中左右边界相关的绕组数可能会有所不同。我们认为，我们在这里提出的处方也可以应用于其他1D多波段系统。
We use multi-band SSH models to demonstrate a prescription for calculating the correct Zak phase and winding number of multi-band systems. We verify our prescription by comparing the resultant winding number of a four-band SSH model with the edge states of a semi-infinite chain which we find by solving the equation of motion. We then also carry out an extensive comparison with the numerical results obtained by solving the matrix eigenvalue problem of finite chains with various number of sites. As a double check of our prescription, we also confirm the bulk edge correspondence in a six-band SSH model. Similar to the usual SSH model, the winding numbers associated to the left and right boundaries in a finite chain may be different if space inversion symmetry is violated in the system. We believe the prescription we propose here may also be applied to other 1D multi-band systems.
