论文标题
平坦状态在具有平坦波段的非温和无序晶格模型中平坦状态的定位和重点定位
Delocalization and re-entrant localization of flat-band states in non-Hermitian disordered lattice models with flat bands
论文作者
论文摘要
我们提出了一项关于安德森（Anderson）定位的数值研究，该定位在具有平坦带的无序的非热晶格模型中。具体而言，我们考虑具有随机标量电势和统一的想象矢量电位的一维存根和二维Kagome晶格，并计算复杂能量的光谱，参与比和绕组数是虚构矢量电位强度的函数，$ h $。发现平面状态显示出从本地化到DELEACALIGAL的双重过渡，再到$ H $的局部状态，与经过单个Dellocalization过渡的分散带状态相反。当$ h $足够小时，所有平发状态都是本地化的。随着$ h $的增加，高于某个临界值$ h_1 $，一些平面状态被拆卸。与之相关的参与率大大增加，其绕组数量为非零。随着$ h $的进一步增加，越来越多的平坦国家将被定位为DELABALIAL，直到DELEACALIDED State的比例达到最大值。对于较大的$ h $值，进行了重新输入本地化，在另一个关键值$ H_2 $下，所有平面状态都返回到紧凑的本地化状态，参与率很小，绕线数为零。这种重点定位过渡是由于疾病，非热性和平坦带之间的相互作用引起的，是许多具有虚构矢量电势和平坦带的模型中发生的现象。我们通过计算局部密度分布来探讨平流状态的空间特性。
We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically we consider one-dimensional stub and two-dimensional kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, $h$. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with $h$, in contrast to the dispersive-band states going through a single delocalization transition. When $h$ is sufficiently small, all flat-band states are localized. As $h$ increases above a certain critical value $h_1$, some pair of flat-band states become delocalized. The participation ratio associated with them increases substantially and their winding numbers become nonzero. As $h$ increases further, more and more flat-band states get delocalized until the fraction of the delocalized states reaches a maximum. For larger $h$ values, a re-entrant localization takes place and, at another critical value $h_2$, all flat-band states return to compact localized states with very small participation ratios and zero winding numbers. This re-entrant localization transition, which is due to the interplay among disorder, non-Hermiticity, and flat band, is a phenomenon occurring in many models having an imaginary vector potential and a flat band simultaneously. We explore the spatial characteristics of the flat-band states by calculating the local density distribution.
