论文标题
三维扩展的Lieb晶格中的定位，阶段和过渡
Localization, phases and transitions in the three-dimensional extended Lieb lattices
论文作者
论文摘要
我们研究了3D Lieb晶格中的本地化属性和Anderson过渡，在存在障碍的情况下，我们在3D Lieb晶格{L} _3（1）$及其扩展$ \ Mathcal {l} _3（n）$中。我们计算扁平带的位置，状态的无序密度以及多达4个不同的Lieb晶格的能量驱动相图。通过有限尺寸的缩放，我们获得了关键属性，例如关键疾病和能量以及通用定位长度指数$ν$。我们发现，关键障碍$ W_C $从$ \ sim 16.5 $降低到$ \ sim 8.6 $ for $ \ mathcal {l} _3（1）$，$ \ sim 5.9 $ for $ \ nathcal {lathcal {l}然而，关键指数$ν$的价值对于在此处研究的所有LIEB晶格，以及在错误栏中均与普遍接受的通用值$ν= 1.590（1.579,1.602）$相同。
We study the localization properties and the Anderson transition in the 3D Lieb lattice $\mathcal{L}_3(1)$ and its extensions $\mathcal{L}_3(n)$ in the presence of disorder. We compute the positions of the flat bands, the disorder-broadened density of states and the energy-disorder phase diagrams for up to 4 different such Lieb lattices. Via finite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent $ν$. We find that the critical disorder $W_c$ decreases from $\sim 16.5$ for the cubic lattice, to $\sim 8.6$ for $\mathcal{L}_3(1)$, $\sim 5.9$ for $\mathcal{L}_3(2)$ and $\sim 4.8$ for $\mathcal{L}_3(3)$. Nevertheless, the value of the critical exponent $ν$ for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value $ν=1.590 (1.579,1.602)$.
