SciPost Submission Page

Correlations of quantum curvature and variance of Chern numbers

by Omri Gat, Michael Wilkinson

Submission summary

As Contributors: Michael Wilkinson
Arxiv Link: https://arxiv.org/abs/2012.03884v2 (pdf)
Date accepted: 2021-06-04
Date submitted: 2021-05-20 00:47
Submitted by: Wilkinson, Michael
Submitted to: SciPost Physics
Academic field: Physics
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)



Login to report or comment