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Correlations of quantum curvature and variance of Chern numbers
by Omri Gat, Michael Wilkinson
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Submission summary
| Authors (as registered SciPost users): | Michael Wilkinson |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2012.03884v2 (pdf) |
| Date accepted: | June 4, 2021 |
| Date submitted: | May 20, 2021, 12:47 a.m. |
| Submitted by: | Michael Wilkinson |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| 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)