Quasiparticle spectra and specific heat of a normal Fermi liquid in a spin-fluctuation model.

Abstract

We calculate statistical and dynamical quasiparticle energies of a normal Fermi liquid in a spin-fluctuation model. The properties of spin fluctuations in the model are the same as those given by Landau Fermi-liquid theory at long wavelengths, low frequencies, and low temperatures if all Landau parameters except ${F}_{0}^{a}$ are neglected. The statistical quasiparticle spectrum is found to be significantly less dependent on momentum and temperature than the dynamical quasiparticle one. The specific heat is calculated both from the statistical quasiparticle spectrum and from the thermodynamic potential, and for parameters appropriate for liquid $^{3}\mathrm{He}$, the corrections to the leading low-temperature result (\ensuremath{\propto}T) are well characterized by ${T}^{3}$lnT behavior up to temperatures of order 100 mK, which is in qualitative agreement with what Greywall finds experimentally. If the Landau parameter ${F}_{1}^{a}$ is included in the calculation in addition to ${F}_{0}^{a}$, we find rather good agreement between theory and experiment. A further conclusion of our work is that the finite-temperature contributions to the specific heat are much less sensitive to variations of the cutoff momentum in our calculations than is the spin-fluctuation contribution to the effective mass. Spin fluctuations are therefore able to account for finite-temperature effects, even though they provide only a modest contribution to the effective mass. We also investigate the reason for earlier calculations in the paramagnon model giving very low estimates of the temperature below which the specific heat should exhibit ${T}^{3}$lnT behavior, and find that this is due to (i) the fact that the dynamical quasiparticle contribution to the specific heat was calculated and (ii) the use of the paramagnon model, rather than Landau theory.