Interactions, Localization, and the Integer Quantum Hall Effect

We report on numerical studies of the influence of Coulomb interactions on the localization of electronic wave functions in a strong magnetic field. Interactions are treated in the Hartree-Fock approximation. Localization properties are studied both by evaluating participation ratios of Hartree-Fock eigenfunctions and by studying the boundary-condition dependence of Hartree-Fock eigenvalues. We find that interactions have no effect on the critical exponent characterizing the diverging localization length, no effect on the fractal dimension of the second moment of the extended wave functions, and no effect on Thouless number estimates of the maximum dissipative conductivity.