SINGULARITIES IN THE FERMI-LIQUID DESCRIPTION OF A PARTIALLY FILLED LANDAU-LEVEL AND THE ENERGY GAPS OF FRACTIONAL QUANTUM HALL STATES

We consider a two-dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. U sing a fermionic Chern-Simons approach, we study the description of th e system's low energy excitations within an extension of Landau's Ferm i-liquid theory. We calculate perturbatively the effective mass and th e quasiparticle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion's eff ective mass diverges logarithmically at the Fermi level, and argue tha t this divergence allows for an exact calculation of the energy gaps o f the fractional quantized Hall states asymptotically approaching thes e filling fractions. We find that the quasiparticle interaction functi on approaches a delta function. This singular behavior leads to a canc ellation of the diverging effective mass from the long-wavelength low- frequency linear response functions at even denominator filling fracti ons.