Correlations of quantum curvature and variance of Chern numbers
Disordered Systems and Neural Networks
2021-06-23 v2 Quantum Physics
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.
Keywords
Cite
@article{arxiv.2012.03884,
title = {Correlations of quantum curvature and variance of Chern numbers},
author = {Omri Gat and Michael Wilkinson},
journal= {arXiv preprint arXiv:2012.03884},
year = {2021}
}
Comments
24 pages, 10 figures, submitted to Sci. Post Physics, minor revision in response to referee reports