量子临界点附近电流-电流关联函数的映射
Mapping the Current-Current Correlation Function Near a Quantum Critical Point
摘要：
电流-电流关联函数是均匀固体中电子输运理论中的一个有用概念。有限温度下的电导率张量以及安德森的局域化长度可以完全从这个关联函数计算。基于这两个物理量在整数量子霍尔效应中的平台-绝缘体或平台-平台跃迁附近的临界行为，我们导出了电流-电流关联函数的渐近公式，从而使我们能够对其一般行为作出一些理论预测.对于无序的Hofstadter模型，我们利用数值模拟映射了电流-电流关联函数，得到了其在临界点附近的渐近形式，证实了理论预言.
英文摘要：
The current-current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson's localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau-insulator or plateau-plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current-current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current-current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.
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