Variational and Green's Function Monte Carlo Study of Lightly Doped Quantum Antiferromagnets

The two-dimensional t-J model on the square lattice is studied as a relevant model to capture the essential physics of the high-temperature copper-oxide superconductors. In order to gain understanding of the basic physics of the model, fundamental issues such as the motion of a single hole and the binding of two holes in a quantum antiferromagnet are addressed. A numerical approach is followed, combining a variation calculation with the use of the Green's function Monte Carlo method, applied in this thesis for the first time to study the t-J model in the presence of mobile holes. Important insight is obtained on the effect of a single hole on the antiferromagnetic background and on the occurrence of binding of two holes. It is found that a critical value (t/J) _{c} of the parameter t/J of the model exists such that hole binding no longer takes place for t/J>(t/J)_{c}, with (t/J)_{c}~3.7. The value that t/J should have in the real material is estimated to be about 3, in order for the model to be relevant to superconductivity. Further research developments are discussed.