On the absence of finite size corrections in the quantized Hall conductance

Abstract A connection between the Hall conductance in realistic situations and a topological invariant in the momentum space is pointed out using the von Neumann lattice representation in which Landau level electrons have minimum spatial extensions. We show that the Hall conductance is a unique topological invariant that has no finite size correction and is quantized exactly in the quantum Hall regime where the one-particle states around the Fermi energy are either localized states or one-dimensionally extended states, based on the momentum representation of the σ xy .