Universal Chern number statistics in random matrix fields

Or Swartzberg*, Michael Wilkinson, Omri Gat

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageAmerican English
Article number015
JournalSciPost Physics
Volume15
Issue number1
DOIs
StatePublished - Jul 2023

Bibliographical note

Publisher Copyright:
Copyright © O. Swartzberg et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.

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