This question arises from reading Wen's book "Quantum Field Theory of Many-body Systems (Oxford 2004)" p204
To appreciate the brilliance of Landau-Fermi liquid theory, let us look at the many-body Hamiltonian of interacting electrons, namely $$H= \sum_i \left( \frac{ \hbar^2}{2m} \partial^2_{\mathbf{x}_i}+U(\mathbf{x}_i) \right) + \sum_{i<j} \frac{e^2}{|\mathbf{x}_i-\mathbf{x}_j|} $$
It is hopeless for a theorist to solve such a 'nasty' system, not to mention to guess that such a system behaves almost like a free electron system. Certainly, condensed matter physicists did not provide such a bold guess. It is nature itself who hints to us over and over again that metals behave just like a free electron system, despite the strong Coulomb interaction. Even now, I am amazed that so many metals can be described by Landau Fermi liquid theory, and puzzled by the difficulty to find a metal that cannot be described by Landau Fermi liquid theory.
My question is, is there any attempt to derive Landau Fermi liquid theory from the microscopic Hamiltonian given above? Even from numerical side, is that possible to see the emergence of Landau Fermi liquid theory from first-principle calculation, such as density-functional theory?
