We investigate the probability distribution of Chern numbers (quantum Hall conductance 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 the correlation is weak but slowly-decaying. Also, the statistics of weighted sums of Chern numbers 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.
Bibliographical noteFunding Information:
Funding information MW is grateful for the generous support of the Racah Institute, who funded a visit to Israel. This work was supported by the German-Israeli Foundation for financial support under grant number GIF I-1499-303.7/2019.
Copyright © O. Swartzberg et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.