Study of integer quantum Hall transition in long-ranged potentials

We present results of a numerical study of a two-dimensional system of noninteracting electrons in a random correlated potential in the lowest Landau level in the presence of a perpendicular magnetic field. We use spatially uncorrelated and unbiased random gaussian potentials as well as potentials $V(r) $ with long-range, power-law correlations $\langle V(0)V(r) \rangle \propto r^{-\alpha}$ for different exponents $\alpha$ as models of disorder. We compute the Hall conductance $\sigma_{xy} $ as well as the Thouless conductance as a function of size $L$ of the sample, and use finite size scaling to determine the exponent $\nu$ characterizing the divergence of the localization length $\xi$ at the quantum Hall transition. We also study the scaling of the diagonal conductivity as a function of $L$ and compare our results to those obtained previously through different methods.