Correlations of quantum curvature and variance of Chern numbers

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.

24 pages, 10 figures, submitted to Sci. Post Physics, minor revision in response to referee reports

Cited by in corpus (4)

• Winding Number Statistics of a Parametric Chiral Unitary Random Matrix Ensemble
• Statistical Topology -- Distribution and Density Correlations of Winding Numbers in Chiral Systems
• Universal Chern number statistics in random matrix fields
• Winding Number Statistics for Chiral Random Matrices: Universal Correlations and Statistical Moments in the Unitary Case