Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France.
Phys Rev Lett. 2019 Jan 25;122(3):030401. doi: 10.1103/PhysRevLett.122.030401.
I present the results of extensive numerical simulations, which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches, and chaos. I first show that strong localization confines quantum transport along paths that are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent ζ characterizing the transverse fluctuations of these paths and find that its value ζ=2/3 is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely, the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder and more spin-glass-like behavior at strong disorder.
我呈现了广泛的数值模拟结果，这些结果揭示了在零温度下二维安德森局域化的玻璃态性质：钉扎、雪崩和混沌。我首先表明，强局域化将量子输运限制在由无序钉扎的路径上，但当能量变化时，这些路径会突然发生急剧变化（雪崩）。我确定了描述这些路径横向涨落的粗糙度指数 ζ，发现其值 ζ=2/3 与有向聚合物问题相同。最后，我描述了混沌性质，即电导对无序构型小扰动的脆弱性。它与弱无序时的干涉效应和普适电导涨落以及强无序时更类似于自旋玻璃的行为有关。
