Breakdown of Fermi Liquid in correlated electron systems

The standard description of metals is based on the Landau theory of Fermi systems (Fermi Liquid theory). This picture breaks down in one dimensional systems, which are instead described by the Luttinger Liquid theory. Actually, experimental evidence indicates that Fermi Liquid theory breaks down in a variety of physical systems, including superconducting cuprates. In the first part of this lecture we will consider the relevant problem of crossover from Luttinger to Fermi Liquid with increasing dimensionality, showing that the Fermi Liquid is stable with respect to residual scattering by regular (short range) interactions among quasiparticles in any d > 1. However singular interactions can modify these results and open the way to richer scenarios. Relevant cases of singular interactions concern: i) gauge theories introduced to describe the half-tilled Landau level and spin liquids considered in the context of high T-c cuprates; ii) proximity to a quantum critical point which has been investigated as a source of non-Fermi Liquid behavior in both heavy fermion systems and cuprates. Even though the theory of non-Fermi Liquid in d > 1 is hindered by the lack of exact nonperturbative methods in d not equal 1, various progresses have been made. In particular the singular forward scattering has been approached with some success by both bosonization and renormalization group methods.