  Ground state properties of the Hubbard model on a two-dimensional square
lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate
results for energy, double occupancy, effective hopping, magnetization, and
momentum distribution are calculated for interaction strengths of U/t from 2 to
8, for a range of densities including half-filling and n = 0.3, 0.5, 0.6, 0.75,
and 0.875. At half-filling, the results are numerically exact. Away from
half-filling, the constrained path Monte Carlo method is employed to control
the sign problem. Our results are obtained with several advances in the
computational algorithm, which are described in detail. We discuss the
advantages of generalized Hartree-Fock trial wave functions and its connection
to pairing wave functions, as well as the interplay with different forms of
Hubbard-Stratonovich decompositions. We study the use of different twist angle
sets when applying the twist averaged boundary conditions. We propose the use
of quasi-random sequences, which improves the convergence to the thermodynamic
limit over pseudo-random and other sequences. With it and a careful finite size
scaling analysis, we are able to obtain accurate values of ground state
properties in the thermodynamic limit. Detailed results for finite-sized
systems up to 16 \times 16 are also provided for benchmark purposes.
