The Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions

TL;DR

This paper investigates how electron-electron interactions influence the critical behavior of the integer quantum Hall effect transitions, finding the non-interacting fixed point remains stable under short-range interactions and Coulomb effects are marginal.

Contribution

It provides a renormalization group analysis showing the stability of the non-interacting fixed point against short-range and Coulomb interactions in the integer quantum Hall transitions.

Findings

Non-interacting fixed point is stable with short-range interactions.

Coulomb interactions are marginal perturbations at the Hartree-Fock fixed point.

Renormalization group dimension for short-range interactions is -0.66±0.04.

Abstract

We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $-0.66\pm0.04$. Thus the non-interacting fixed point (characterized $z=2$ and $\nu\approx 2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ($z=1$, $\nu\approx 2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.