  We develop a variant of the density matrix renormalization group (DMRG)
algorithm for two-dimensional cylinders that uses a real space representation
along the cylinder and a momentum space representation in the perpendicular
direction. The mixed representation allows us to use the momentum around the
circumference as a conserved quantity in the DMRG algorithm. Compared with the
traditional purely real-space approach, we find a significant speedup in
computation time and a considerable reduction in memory usage. Applying the
method to the interacting fermionic Hofstadter model, we demonstrate a
reduction in computation time by over 20-fold, in addition to a sixfold memory
reduction.
