Universal temperature corrections to Fermi liquid theory in an interacting electron system

We calculate analytically the effective mass and the quasiparticle renormalization factor in an electron liquid with long-range Coulomb interactions between electrons in two and three dimensions in the leading order density expansion. We concentrate on the temperature dependence of the effective mass in the limit T/T(F)r(s)1 and show that the leading temperature correction is linear in two dimensions and proportional to T (2) ln(1/T) in three dimensions (positive in both cases). We explicitly calculate the coefficients, which are shown to be universal density independent parameters of the order of unity (in the high-density limit). The singular temperature corrections are due to the singularity in the dynamic dielectric function at omegasimilar tov(F)q and q2p(F). In two dimensions, we predict a nonmonotonic effective mass temperature dependence and find that the maximum occurs at a temperature T(*)similar toT(F)r(s) ln(-1)(1/r(s)). We also study the quasiparticle renormalization factor in both three and two dimensions.