论文标题
随机矩阵字段中的通用Chern数量统计
Universal Chern number statistics in random matrix fields
论文作者
论文摘要
我们研究了GUE随机矩阵集合的参数版本的Chern数字（量子Hall效应整数）的概率分布，这是混乱或无序系统的模型。基于较早的研究[O. Gat和M. Wilkinson，Scipost Phys。，10，149，（2021）]的量子绝热曲率的统计数据，当参数相关长度很小时。但是，与较早的猜想相反，我们发现差距Chern数是相关的，并且相关性较弱，但要缓慢付费。同样，基于差距Chern数量不相关的假设，许多频段的Chern数量加权总和的统计数据与预测明显不同。我们所有的结果都与较早的论文中描述的普遍性假设一致，包括在以前未研究的大相关长度方面，而Chern统计数字高度非高斯。
We investigate the probability distribution of Chern numbers (quantum Hall effect integers) for a parametric version of the GUE random matrix ensemble, which is a model for a chaotic or disordered system. The numerically-calculated single-band Chern number statistics agree well with predictions based on an earlier study [O. Gat and M. Wilkinson, SciPost Phys., 10, 149, (2021)] of the statistics of the quantum adiabatic curvature, when the parametric correlation length is small. However, contrary to an earlier conjecture, we find that the gap Chern numbers are correlated, and that correlation is weak but slowly-decaying. Also, the statistics of weighted sums of Chern numbers for many bands differs markedly from predictions based upon the hypothesis that gap Chern numbers are uncorrelated. All our results are consistent with the universality hypothesis described in the earlier paper, including in the previously unstudied regime of large correlation length, where the Chern statistics is highly non-Gaussian.
