论文标题
随机电势的几何形状：量子霍尔高原过渡中2D重力的诱导
Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions
论文作者
论文摘要
在整数量子大厅高原过渡的背景下，我们从随机景观电位上制定了一个特定的图，到2D离散的随机表面。潜力的关键点，即Maxima，minima和Maddle点独特地定义了离散的表面$ s $以及其双$ s^*$由四边形和$ n- $ gonal面制成的，从而将电位的几何形状与离散表面的几何形状联系起来。该地图依赖于费米级别。费米湖的边缘状态沿着邻居鞍点之间的等值轮廓移动，形成了一个散射网络，该网络为高原过渡定义了费米子模型中的几何基础。 Gruzberg，Klümper，Nuding和Sedrakyan最近提出的网络模型表征网络模型的替代概率在当前框架内物理解释为与费米水平相连的参数。
In the context of the Integer Quantum Hall plateau transitions, we formulate a specific map from random landscape potentials onto 2D discrete random surfaces. Critical points of the potential, namely maxima, minima and saddle points uniquely define a discrete surface $S$ and its dual $S^*$ made of quadrangular and $n-$gonal faces, respectively, thereby linking the geometry of the potential with the geometry of discrete surfaces. The map is parameter-dependent on the Fermi level. Edge states of Fermi lakes moving along equipotential contours between neighbour saddle points form a network of scatterings, which define the geometric basis, in the fermionic model, for the plateau transitions. The replacement probability characterizing the network model with geometric disorder recently proposed by Gruzberg, Klümper, Nuding and Sedrakyan, is physically interpreted within the current framework as a parameter connected with the Fermi level.
