论文标题
本地化挑战有限的二维安德森模型中的量子混乱
Localization challenges quantum chaos in the finite two-dimensional Anderson model
论文作者
论文摘要
据认为，二维Anderson模型在热力学极限下对任何非零疾病都表现出定位，并且众所周知，有限尺寸的效应在弱的混乱极限中相当大。在这里，我们使用现代文献中使用的标准指标（例如水平间距比，光谱形式，可观察到的矩阵元素的方差，参与熵和特征环境纠缠透镜）中使用的标准指标，研究有限的2D安德森模型中的量子chaos与定位过渡。我们表明，这些指标的许多特征可能表明在弱疾病中出现健壮的单粒子量子混乱。但是，我们认为，仔细的数值分析与单参数缩放理论一致，并预测了在热力学极限中任何非零疾病价值下量子混乱的分解。在这种分解的标志中，弱体障碍频谱形式的普遍行为，以及各种指标的普遍缩放作为参数$ u = \ left的函数（w \ ln v \ right）^{ - 1} $，其中$ w $是混乱的强度，$ v $是晶格站点的数量。
It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here we numerically study the quantum-chaos to localization transition in the finite 2D Anderson model using standard indicators used in the modern literature such as the level spacing ratio, spectral form factor, variances of observable matrix elements, participation entropy and the eigenstate entanglement entropy. We show that many features of these indicators may indicate emergence of robust single-particle quantum chaos at weak disorder. However, we argue that a careful numerical analysis is consistent with the single-parameter scaling theory and predicts the breakdown of quantum chaos at any nonzero disorder value in the thermodynamic limit. Among the hallmarks of this breakdown are the universal behavior of the spectral form factor at weak disorder, and the universal scaling of various indicators as a function of the parameter $u = \left(W \ln V\right)^{-1}$ where $W$ is the disorder strength and $V$ is the number of lattice sites.
