I will discuss the application of different Quantum Monte Carlo methods to shell model type Hamiltonians. Recently, we calculated the ground state energy of many fp-shell odd-even nuclei using the shell model Monte Carlo method. I will describe how the Green's functions of even particle systems can be used to extract the ground state energy of odd particle systems, thereby circumventing the sign problem due to particle number projection in shell model Monte Carlo. Thereafter, I will discuss the possibility of improving the predictions of density functional theory in nuclei by incorporating the pairing correlations exactly. For this purpose we use a particular projection Monte Carlo method which is free from sign problems for the pairing Hamiltonian. Finally, time permitting, I will talk about the projection (Green's function) Monte Carlo method we are developing for general shell model type Hamiltonians and present some results for cold atomic gases in a harmonic trap.
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