Correlations of quantum curvature and variance of Chern numbers

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)