论文标题
一维镶嵌晶格中的精确迁移率边缘具有缓慢变化的电势
Exact Mobility Edges in One-Dimensional Mosaic Lattices Inlaid with Slowly Varying Potentials
论文作者
论文摘要
我们提出了一个一维镶嵌模型的家族，其潜在的$ v_n =λ\ cos（παn^ν）$，其中$ n $是晶格站点索引，$ 0 <ν<1 $。将渐近启发式论证与传递矩阵的痕量图，迁移率边缘（MES）和伪动力边缘（PME）的痕量映射理论相结合，在其能量谱中是半分析的解决方案，其中我将延伸的状态与弱点的状态分开，PME将弱点分离为弱点的状态。局部密度，Lyapunov指数和定位张量，诊断出扩展，关键，弱点且局部局部化的特征状态的性质。与理论预测的数值计算结果具有良好的定量一致性。
We propose a family of one-dimensional mosaic models inlaid with a slowly varying potential $V_n=λ\cos(παn^ν)$, where $n$ is the lattice site index and $0<ν<1$. Combinating the asymptotic heuristic argument with the theory of trace map of transfer matrix, mobility edges (MEs) and pseudo-mobility edges (PMEs) in their energy spectra are solved semi-analytically, where ME separates extended states from weakly localized ones and PME separates weakly localized states from strongly localized ones. The nature of eigenstates in extended, critical, weakly localized and strongly localized is diagnosed by the local density of states, the Lyapunov exponent, and the localization tensor. Numerical calculation results are in excellent quantitative agreement with theoretical predictions.
