Correlations of quantum curvature and variance of Chern numbers
- URL: http://arxiv.org/abs/2012.03884v2
- Date: Thu, 6 May 2021 11:03:51 GMT
- Title: Correlations of quantum curvature and variance of Chern numbers
- Authors: Omri Gat and Michael Wilkinson
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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