Perturbational Calculation of the Quantum Hall Conductivity

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Abstract
The Hall conductivity in the lowest Landau level is calculated by a large order perturbational expansion. It is shown that it takes the quantized value at the band tail by the analysis of the Borel-Padé summation. From the viewpoint of the renormalization group, the 1/N expansion is also discussed for the longitudinal conductivity and for the Hall conductivity and the logarithmic terms are investigated up to the order of 1/N2.