Correlations of quantum curvature and variance of Chern numbers

Gat, Omri; Wilkinson, Michael

doi:10.21468/SciPostPhys.10.6.149

SciPost Physics

Correlations of quantum curvature and variance of Chern numbers

Omri Gat, Michael Wilkinson

SciPost Phys. 10, 149 (2021) · published 21 June 2021

doi: 10.21468/SciPostPhys.10.6.149
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.10.6.149
TI  - Correlations of quantum curvature and variance of Chern numbers
PY  - 2021/06/21
UR  - https://scipost.org/SciPostPhys.10.6.149
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 10
IS  - 6
SP  - 149
A1  - Gat, Omri
AU  - Wilkinson, Michael
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.10.6.149,
	title={{Correlations of quantum curvature and variance of Chern numbers}},
	author={Omri Gat and Michael Wilkinson},
	journal={SciPost Phys.},
	volume={10},
	pages={149},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.10.6.149},
	url={https://scipost.org/10.21468/SciPostPhys.10.6.149},
}

Cited by 4

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¹ Omri Gat,
² ³ Michael Wilkinson

Funder for the research work leading to this publication

German-Israeli Foundation for Scientific Research and Development [GIF]