论文标题
在Aubry-André-Harper调制的情况下，远程Kitaev链的本地化和多重分子特性
Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
论文作者
论文摘要
在存在准碘电位的情况下，著名的基塔夫链呈现出具有崇高，局部和多重型状态的有趣相图。在这项工作中，我们通过研究远程跳和超导配对振幅的情况下研究Aubry-André-Harper模型的定位特性来概括这些结果。这些振幅分别损失了幂律指数$ξ$和$α$。为此，我们审查并比较了一个全球和局部特征方法的工具箱，以研究千古，局部和多重分子状态之间的不同类型的过渡。我们报告了能量依赖性的转变，以与$α<1 $配对术语以及能量依赖性的术语以及从ergodic到局部状态的术语，具有中间多型区域，$α> 1 $。中间多重区域的大小不仅取决于超导配对项$δ$的值，还取决于能量频段。过渡不是由移动性边缘描述，而是我们报告具有不同类型本地化属性的频段的杂交。这导致了分形维度遵循不同分布的多重分子状态共存。
In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization properties of the Aubry-André-Harper model in the presence of long-range hopping and superconducting pairing amplitudes. These amplitudes decay with power-law exponents $ξ$ and $α$ respectively. To this end, we review and compare a toolbox of global and local characterization methods in order to investigate different types of transitions between ergodic, localized and multifractal states. We report energy-dependent transitions from ergodic to multifractal states for pairing terms with $α<1$ and energy-dependent transitions from ergodic to localized states with an intermediate multifractal region for $α>1$. The size of the intermediate multifractal region depends not only on the value of the superconducting pairing term $Δ$, but also on the energy band. The transitions are not described by a mobility edge, but instead we report hybridization of bands with different types of localization properties. This leads to coexisting multifractal regimes where fractal dimensions follow different distributions.
