UC Santa Cruz

The primary aim of this thesis is to understand the effects of electronic frustration generated by local interactions of the Hubbard U type on a lattice. Specifically we attempt to study the strongly interacting liquid phase of the Hubbard model and the so called extremely correlated phase of the t-J model without any broken symmetries. Of particular interest is the fate of the Fermi Liquid state under the influence of a large U. Exact solutions in solvable limits inform most of the physical intuition. Perturbative methods such as an infinite order calculation in the particle-particle channel ladder expansion yield fruitful results. Finally the non-perturbative field theory of Schwinger is used to generate a calculation scheme for the Green's function of the non-canonical Fermions of the t-J model. Numerical results are compared with important experimental results from the high-T_c Cuprate compounds.