Dynamical Properties of Strongly Correlated Fermionic Systems

The Exact Diagonalization method is a powerful numerical tool to study Quantum Many Body systems on nite clusters. In particular, using this technique one can accurately calculate energy and momentum dependent dynamic correlation functions which are observable in scattering experiments, such as Neutron Scattering, Raman Scattering, and Photoemission Spectroscopy which measures the spectral function of the system. Here we give an outline of the Lanczos method with special emphasis on the evaluation of dynamical quantities. In this thesis, we apply this method to two-dimensional models of strongly correlated electrons which are believed to describe the physics of the recently discovered cuprate high-Tc compounds. We show that simple models of strongly correlated electrons, such as the Hubbard and the t-J model, can account for some normal state properties of these materials. In particular, the occurance of photoemission bands which are introduced by short-range antiferromagnetic correlations is discussed. The precursor materials of the cuprate superconducters are antiferromagnets. Here, we address the properties of antiferromagnets as they evolve from an insulating to a metallic phase upon doping. We focus on the shape of the Fermi surface at small hole doping and on the in uence of long-range Coulomb interactions on the occurance of superconducting and charge density wave phases. We also investigate systems in one spatial dimension where mechanisms similar to the ones in higher dimensions can be studied on larger clusters. However, there xii are some signi cant dimension dependent di erences, e.g. in contrast to the twodimensional case, one-dimensional antiferromagnets exhibit a gapped spectrum if the participating spins have integer value. We discuss the physics of these `Haldane' chains. The calculated spectra for these materials are in excellent agreement with recent Neutron Scattering Experiments. The e ect of random exchange interaction in quantum antiferromagnets is also discussed. We show that such interactions do not necessarily induce an exponential decay in the spin correlations. Also, we argue that random exchange interactions can be induced by phononic disorder and might be responsible for the lineshape of Raman spectra observed in the cuprates. Our calculated Raman spectra are in good agreement with recent experiments on various cuprate precursors. xiii CHAPTER