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arXiv · 2012.03884

Correlations of quantum curvature and variance of Chern numbers

Omri Gat·Michael Wilkinson
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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.

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Omri Gat, Michael Wilkinson. 2020-12-07. Correlations of quantum curvature and variance of Chern numbers. https://doi.org/10.21468/scipostphys.10.6.149

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