Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

TL;DR

This study investigates how short-range electron-electron interactions affect the scaling behavior and transport properties near integer quantum Hall transitions, revealing discontinuous changes and unique scaling variables despite their irrelevance at the fixed point.

Contribution

It demonstrates that short-range interactions cause a discontinuous change in transport and alter the scaling variables near the quantum Hall transition, despite being irrelevant at the fixed point.

Findings

Conductivity is zero without interactions but non-zero with weak interactions.

Scaling depends on the variable ω/T^p, not ω/T, due to interactions.

Derived expressions for inelastic exponent p and thermal exponent z_T in terms of scaling dimensions.

Abstract

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $\omega$, and temperature, $T$, is determined by the scaling variable $\omega/T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\omega/T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-\alpha < 0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2\alpha/z$ and $z_T=2/p$.