# Correlations of quantum curvature and variance of Chern numbers

### Submission summary

 Authors (as Contributors): Michael Wilkinson
Submission information
Date accepted: 2021-06-04
Date submitted: 2021-05-20 00:47
Submitted by: Wilkinson, Michael
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
Approaches: Theoretical, Computational

### Abstract

We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse of the distance at small separations. We also define and analyse a correlation function of mixed states, showing that it is finite but singular at small separations. A scaling hypothesis on a universal form for both types of correlations is supported by Monte-Carlo simulations. We relate the correlation function of the curvature to the variance of Chern integers which can describe quantised Hall conductance.

Published as SciPost Phys. 10, 149 (2021)