  In order to extend the density-matrix renormalization-group (DMRG) method to
two-dimensional systems, we formulate two alternative methods to prepare the
initial states. We find that the number of states that is needed for accurate
energy calculations grows exponentially with the linear system size. We also
analyze how the states kept in the DMRG method manage to preserve both the
intrablock and interblock Hamiltonians, which is the key to the high accuracy
of the method. We also prove that the energy calculated on a finite cluster is
always a variational upper bound.
