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Correlations of quantum curvature and variance of Chern numbers
by Omri Gat, Michael Wilkinson
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint 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 |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- Condensed Matter Physics - Theory
|
| 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.
