Singularities in the Fermi-liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states

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Abstract
We consider a two-dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern-Simons approach, we study the description of the system’s low energy excitations within an extension of Landau’s Fermi-liquid theory. We calculate perturbatively the effective mass and the quasiparticle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion’s effective mass diverges logarithmically at the Fermi level, and argue that this divergence allows for an exact calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions. We find that the quasiparticle interaction function approaches a δ function. This singular behavior leads to a cancellation of the diverging effective mass from the long-wavelength low-frequency linear response functions at even denominator filling fractions.