Quantum Simulations of the Ground State of the One-Dimensional Hubbard Model.

In this dissertation we have investigated the ground state of the one dimensional Hubbard model, a popular model to represent electronic structure of quasi-one-dimensional conductors. The methods we have used in this study are the Green's Function Monte Carlo (GFMC) method and the Variational Monte Carlo (VMC) method. The most significant outcome of this investigation is the development of a lattice version of the GFMC method which can provide exact treatment of a class of Hamiltonians for which other exact approaches are not possible. In particular we have obtained, for the first time, the exact ground state energies for the extended Hubbard model. To further study the ground state structure of this model we have calculated the density -density and the spin-spin correlation functions and found evidence of Charge Density Waves and Spin Density Waves in the expected interaction regimes. We have also studied the effect of magnetization on the exact ground state energies as well as on the ground state correlation functions.