In this thesis, we present theoretical analysis of Fermi liquid theory for Hubbard model on a triangular lattice. In particular, the wavefunction and Landau parameters for the system are calculated and analyzed. We start with calculations of the wavefunction and Landau parameters in perturbation theory, both numerically and analytically (for some special cases). The calculation will then be promoted to a variation calculation by modifying the coefficients in the perturbed wavefunction in the perturbation theory. Numerical results for the wavefunction and Landau parameters will be presented. Comparisons between perturbation and variation calculations will be carried out in different scenario, for example, different spatial direction so as to predict the general features of variation refinement of the problem given above.
A numerical method has been developed to solve the RPA equation, exchange term included, in nuclear matter. The dynamic form factor S(q, ω) is extracted for several v4 and v6 phenomenological potentials, including the d1-potential of Gogny et al. The limits of validity of the long-wavelength (Landau) approximation and the often adopted local-kernel approximation are discussed. Substantial disagreements with the exact results are found for the latter. The method is then applied to solve a Jastrow-correlated extension of the RPA equation, using the hardcore OMY potential. Results of calculations performed in two-body cluster approximation and Fermi-Hypernetted-Chain (FHNC) approximation are compared. The two-body results predict an instability against density fluctuations, which disappears at the FHNC level. The validity and consequences of employing the FHNC effective potential within the self-consistent HF/RPA framework are discussed. Future developments include applying the method to other Fermi systems such as liquid 3He and the microscopic calculation of Landau parameters.