  We investigate the application of the Density Matrix Renormalization Group
(DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional
models with dispersion relations corresponding to nearest-neighbor hopping and
$1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor
hopping. By comparing with the exact solutions for both one-dimensional models
and with exact diagonalization in two dimensions, we first investigate the
convergence of the ground-state energy. We find variational convergence of the
energy with the number of states kept for all models and parameter sets. In
contrast to the real-space algorithm, the accuracy becomes rapidly worse with
increasing interaction and is not significantly better at half filling. We
compare the results for different dispersion relations at fixed interaction
strength over bandwidth and find that extending the range of the hopping in one
dimension has little effect, but that changing the dimensionality from one to
two leads to lower accuracy at weak to moderate interaction strength. In the
one-dimensional models at half-filling, we also investigate the behavior of the
single-particle gap, the dispersion of spinon excitations, and the momentum
distribution function. For the single-particle gap, we find that proper
extrapolation in the number of states kept is important. For the spinon
dispersion, we find that good agreement with the exact forms can be achieved at
weak coupling if the large momentum-dependent finite-size effects are taken
into account for nearest-neighbor hopping. For the momentum distribution, we
compare with various weak-coupling and strong-coupling approximations and
discuss the importance of finite-size effects as well as the accuracy of the
DMRG.
