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 Log(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. The singular temperature corrections are due to the singularity in the dynamic dielectric function. In two dimensions, we predict a non-monotonic effective mass temperature dependence and find that the maximum occurs at a temperature T* ~ (T_F r_s)/Log(1/r_s). We also study the quasiparticle renormalization factor in both three and two dimensions.