English

Mapping the Current-Current Correlation Function Near a Quantum Critical Point

Disordered Systems and Neural Networks 2016-02-23 v1

Abstract

The current-current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson's localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau-insulator or plateau-plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current-current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current-current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.

Keywords

Cite

@article{arxiv.1512.02476,
  title  = {Mapping the Current-Current Correlation Function Near a Quantum Critical Point},
  author = {Emil Prodan and Jean Bellissard},
  journal= {arXiv preprint arXiv:1512.02476},
  year   = {2016}
}
R2 v1 2026-06-22T12:04:14.965Z