We calculate, using perturbative calculations and Ward identities, the basic parameters of the Fermi liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model of two-dimensional (2D) fermions with a short-ranged interaction at nonzero temperature. The leading temperature dependence of the spin components of the scattering vertex, the Landau function, and the spin susceptibility is found to be linear. We find that the standard
T=0 relationships for a Galilean-invariant Fermi liquid are violated by finite-temperature terms. The coefficients in the temperature corrections to these relationships involve a subtle interplay between contributions from small and large $(\ensuremath{\sim}{2k}_{F})$ momentum processes. A connection with previous studies of the 2D Fermi-liquid parameters is discussed. We conclude that the linear leading temperature dependence of the parameters is a generic feature of the 2D Fermi liquid.
Finding the distinct features of the crossover from the regime of large overlapping Cooper pairs to the limit of non-overlapping pairs of fermions (Shafroth pairs) in multi-component Fermi systems remains a topical problem in a quantum many-body theory. Here this transition is studied by calculating the two-body density, spin and isospin correlation functions in dilute two-component Fermi superfluid, taking as an example an infinite system of protons and neutrons (nuclear matter). It is shown that criterion of the crossover [Phys. Rev. Lett. 95, 090402 (2005)], formulated for ultracold fermionic atomic gases and consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC–BCS transition at finite isospin asymmetry or finite temperature. As an unambiguous signature of the BEC–BCS transition, one can use the presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states.
Correlated density matrix theory is generalized to investigate equilibrium properties of normal Fermi Liquids such as 3He and nuclear matter at nonzero temperatures. The results also generalize the Fermi-hypernetted-chain technique that is familiar from studies of the ground state of correlated fermions. By employing the concept of renormalized bosons and fermions the formal results are cast in a form that permits the direct evaluation of the statistical properties of the correlated liquid such as the entropy and the specific heat at constant volume among other quantities.