The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid--real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at
n=0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both
U/t=4.0 and
8.0. We find that the strength of the charge ordering depends on
U/t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground-state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum Monte Carlo results. It is shown that the momentum-space DMRG is a very useful numerical tool for studying the Hubbard model and other fundamental models of interacting electrons in two dimensions. For the Hubbard model in two dimensions, the momentum-space DMRG method reproduces accurately the exact diagonalization results of ground-state energies on a 4\ifmmode\times\else\texttimes\fi{}4 lattice and yields new upper bounds of ground-state energies on an 8\ifmmode\times\else\texttimes\fi{}8 lattice.