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.
| Original language | American English |
|---|---|
| Article number | 149 |
| Journal | SciPost Physics |
| Volume | 10 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2021 |
Bibliographical note
Funding Information:OG thanks the German-Israeli Foundation for financial support under grant number GIF I-1499-303.7/2019.
Funding Information:
MW is grateful for the generous support of the Racah Institute, who funded a visit to Israel. Both authors are grateful to the Heilbronn Institute and Prof. Jonathan Robbins at the University of Bristol, who organised a workshop where this research was initiated. OG benefitted
Publisher Copyright:
© O. Gat and M. Wilkinson.