论文标题
开放晶体线性1D紧密结合模型的分析解决方案
Analytical solution of open crystalline linear 1D tight-binding models
论文作者
论文摘要
在此处介绍了一种在开放边界条件下找到所有相应的Aubry-André/Harper单粒子模型的散装和边缘能级的确切分析解决方案的方法，包括整数和非直体单位单元格。最终发现该解决方案取决于相对因素的行为，而这些相关公式（此处提供的紧凑型公式）使此方法易于实现计算。该派生采用了这些模型的哈密顿量的特性，所有这些模型都可以写成Hermitian Block-Tridiagonal toeplitz矩阵。能量谱的概念被推广，以结合散装和边缘带，后者是复杂动量的函数。然后将该方法扩展以求解这些链之一在一端耦合到任意群集/杂质的情况。讨论了基于这些结果的未来发展。
A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-André/Harper single-particle models under open boundary conditions is presented here, both for integer and non-integer number of unit cells. The solutions are ultimately found to be dependent on the behavior of phase factors whose compact formulas, provided here, make this method simple to implement computationally. The derivation employs the properties of the Hamiltonians of these models, all of which can be written as Hermitian block-tridiagonal Toeplitz matrices. The concept of energy spectrum is generalized to incorporate both bulk and edge bands, where the latter are a function of a complex momentum. The method is then extended to solve the case where one of these chains is coupled at one end to an arbitrary cluster/impurity. Future developments based on these results are discussed.
