Specific heat of a normal Fermi liquid. II. Microscopic approach

Abstract

We consider the thermodynamic properties of a normal Fermi liquid, starting from the expression for the thermodynamic potential in terms of the fully renormalized single-particle propagator. It is shown that the entropy may be expressed as the dynamical quasiparticle contribution, given by the usual quasiparticle result for the entropy evaluated using as quasiparticle energies the poles of the single-particle propagator, plus a correction term. The correction term is shown to come from terms in perturbation theory which have at least two vanishing energy denominators. Using a reduced-graph technique similar to that used for analyzing analytic properties of Feynman amplitudes in field theory we investigate in detail the terms which have two vanishing energy denominators. The results are then applied to calculate the contribution from long-wavelength fluctuations to the ${T}^{3}$ $\mathrm{ln}T$ term in the specific heat of a normal Fermi liquid; agreement is obtained with earlier calculations based on Landau Fermi-liquid theory. The differences between various definitions of the quasiparticle energy, and the effect of quasiparticle lifetimes on thermodynamic properties are also considered.