Coulomb interactions at quantum Hall critical points of systems in a periodic potential

TL;DR

This paper investigates how long-range Coulomb interactions influence the critical points between quantum Hall states and insulators, revealing different behaviors depending on the fractional or integer nature of the quantum Hall states.

Contribution

It introduces a low energy theoretical framework for analyzing Coulomb effects at quantum Hall critical points in systems with periodic potentials, highlighting new fixed points and flow behaviors.

Findings

Coulomb interactions are marginally irrelevant for integer quantum Hall transitions.

For fractional cases, behavior varies with anyon statistics, leading to new fixed points or strong coupling flows.

The study identifies stable critical exponents and flow regimes in the presence of Coulomb interactions.

Abstract

We study the consequences of long-range Coulomb interactions at the critical points between integer/fractional quantum Hall states and an insulator. We use low energy theories for such transitions in anyon gases in the presence of an external periodic potential. We find that Coulomb interactions are marginally irrelevant for the integer quantum Hall case. For the fractional case, depending upon the anyon statistics parameter, we find behavior similar to the integer case, or flow to a novel line of fixed points with exponents $z=1$, $\nu > 1$ stable against weak disorder in the position of the critical point, or run-away flow to strong coupling.