Abstract
The quantum Hall system in the lowest Landau level including the Zeeman term is studied by a two-state model, which has a chiral invariance. Using a diagrammatic analysis, we examine this two-state model with random impurity scattering and obtain the exact value of the conductivity at the Zeeman energy E=\ensuremath{\Delta}. We further study the conductivity at another extended state E=${\mathrm{E}}_{1}$ (${\mathrm{E}}_{1}$>\ensuremath{\Delta}). We find that the values of the conductivities at E=\ensuremath{\Delta} and E=${\mathrm{E}}_{1}$ do not depend upon the value of the Zeeman energy \ensuremath{\Delta}. We discuss also the case where the Zeeman energy \ensuremath{\Delta} becomes a random field.
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