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

TL;DR

This paper analytically derives the temperature dependence of effective mass and quasiparticle renormalization in an electron liquid with Coulomb interactions, revealing universal, dimension-specific temperature corrections and non-monotonic behavior in two dimensions.

Contribution

It provides the first analytical calculation of temperature corrections to effective mass and quasiparticle renormalization in Coulomb-interacting electron liquids in 2D and 3D, including universal coefficients.

Findings

Linear temperature correction to effective mass in 2D.

T^2 Log(1/T) correction in 3D.

Non-monotonic effective mass temperature dependence in 2D.

Abstract

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.