SciPost Submission Page
Correlations of quantum curvature and variance of Chern numbers
by Omri Gat, Michael Wilkinson
- Published as SciPost Phys. 10, 149 (2021)
Submission summary
| As Contributors: | Michael Wilkinson |
| Arxiv Link: | https://arxiv.org/abs/2012.03884v2 (pdf) |
| Date accepted: | 2021-06-04 |
| Date submitted: | 2021-05-20 00:47 |
| Submitted by: | Wilkinson, Michael |
| Submitted to: | SciPost Physics |
| 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)