| In recent years, there has been growing interest in the physics of doped Mott-insulators in connection with high-Tc, superconductors. One of the simplest models that captures the essential physics is the two-dimensional Hubbard model with large on-site Coulomb repulsion U. In the absence of a natural small parameter, this and other relevant models of strong correlation have been extended and studied under large symmetry groups (large N) or large dimensions (large d). A generic feature of strong correlation is the coexistence of coherent quasiparticles and the broad incoherent Mott-Hubbard excitations that carry the main part of the spectral weight at small doping.;To capture the important physics due to strong correlations, in this thesis the infinite-U limit of the 2D Hubbard model is studied. In this limit there is a constraint of no double occupancy at any site, which is dealt with by introducing local gauge degrees of freedom. In this work there is a study of the interactions between the quasiparticles and the Mott-Hubbard excitations, and their effects on the low energy properties of this model, using the non-perturbative large N expansion approach. In particular the interest was in seeing if these interactions could lead to a breakdown of the Fermi liquid theory. Within this expansion, these effects first occur in the next to leading order in 1/N, which is carried out completely for the first time.;The main technical advance made here is the development of a theoretical framework to correctly study these 1/N fluctuations. Using this framework, the scattering phase shift, free energy, quasiparticle weight Z, mass renormalization, and the compressibility are calculated, using a combination of analytical and numerical analysis. It is found that while Z and the quasiparticle density of states are weakly renormalized, the chemical potential as a function of doping exhibits a strongly renormalized compressibility which diverges at a finite critical doping delta c = 0.07 +/- 0.01. It is found that this instability is due to enhanced interactions between the quasiparticles, which could lead to phase separation between a ferromagnetic hole poor region, and a paramagnetic hole rich region, with a possibility of superconductivity in either/both regions. |
