We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of two spin-half frustrated spin systems: the triangular and the J1 - J2 Heisenberg antiferromagnets. These are the simplest examples of two-dimensional spin models in which quantum effects may be strong enough to destroy the classical long-range Néel order, thus stabilizing a ground state with symmetries and correlations different from their classical counterparts. In this thesis the ground-state properties of these frustrated models are studied using finitesize spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In particular, in order to control the sign-problem instability, which affects the numerical simulation of frustrated spin systems and fermionic models, we have used the recently developed Green function Monte Carlo with Stochastic Reconfiguration. This technique, which represents the state-of-the-art among the zero-temperature quantum Monte Carlo methods, has been developed and tested in
detail in the present thesis.
