Short-range interactions and scaling near integer quantum Hall transitions

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 noninteracting 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 nonzero 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 $-\alpha <0\mathrm{}$ of the interaction strength and the dynamical exponent z (which has the value $z=2),$ obtaining $p=1+2\mathrm{}\alpha /z$ and $z_T=2/p.\mathrm{}$