The strong electron electron correlation in the Copper Oxygen layers of the high temperature superconductors has been suggested as a possible explanation for the occurrence of superconductivity in these materials. Under this assumption a proposed model to describe the interplay between antiferromagnetism and superconductivity is the two dimensional t-Jmodel.
In this thesis the ground state properties of this model have been studied using exact diagonalization and quantum Monte Carlo simulations. In fermionic systems quantum Monte Carlo methods are affected by the "minus sign problem" instability that makes simulations prohibitive and even impossible at low enough temperature. In order to overcome this difficulty some approximations are necessary, such as the fixed node approximation or the recently proposed
Green function Monte Carlo with stochastic reconfiguration. In this work the first successful application of the latter technique to fermionic system is presented.
It is shown that the two dimensional t-J model, in the physical parameter region, reproduces qualitatively the main experimental features of the high Tc superconductors: d-wave superconducting correlations are strongly enhanced upon small doping (delta) and clear evidence of off-diagonal long range order is found at optimal doping. Antiferromagnetic correlations, clearly present for
the undoped system, are strongly suppressed at small hole density with clear absence of long range order from delta >=0.1.
The possible presence of charge density wave or phase separation instabilities has been investigated. No one of such features has been detected in the physical region, being the homogeneous state the most stable one. Nevertheless the large compressibility suggests that the charge excitations are very close in
energy so that small lattice deformations can easily induce the experimentally observed stripes in the system.
The results of this work strongly support the idea of a pairing force driven only by the electron electron correlation that, upon doping, leads the system from an antiferromagnetic Mott insulator to a superconductor.
