论文标题
$ \ MATHCAL {L}^2 $用于高度激发状态的本地化景观
$\mathcal{L}^2$ localization landscape for highly-excited states
论文作者
论文摘要
本地化景观可直接访问非相互作用无序系统中带底本征的定位。我们通过引入修改后的$ \ Mathcal {l}^2 $ - landscape，将这种方法推广到具有或没有内部自由度的系统中的任意能量的特征状态，我们在一个和二维的Anderson定位的各种原型模型中证明了它的准确性。可以使用分层方法有效地计算此$ \ MATHCAL {L}^2 $ - landscape函数，以评估精心挑选的绿色功能的对角线。我们将我们的方法比较其他景观方法，从而带来了对它们的优势和局限性的新见解。我们的方法是一般的，原则上可以应用于拓扑安德森过渡和多体定位的两项研究。
The localization landscape gives direct access to the localization of bottom-of-band eigenstates in non-interacting disordered systems. We generalize this approach to eigenstates at arbitrary energies in systems with or without internal degrees of freedom by introducing a modified $\mathcal{L}^2$-landscape, and we demonstrate its accuracy in a variety of archetypal models of Anderson localization in one and two dimensions. This $\mathcal{L}^2$-landscape function can be efficiently computed using hierarchical methods that allow evaluating the diagonal of a well-chosen Green function. We compare our approach to other landscape methods, bringing new insights on their strengths and limitations. Our approach is general and can in principle be applied to both studies of topological Anderson transitions and many-body localization.
