Correlations of quantum curvature and variance of Chern numbers

Omri Gat*, Michael Wilkinson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageAmerican English
Article number149
JournalSciPost Physics
Issue number6
StatePublished - Jun 2021

Bibliographical note

Publisher Copyright:
© O. Gat and M. Wilkinson.


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