Single-block renormalization group: quantum mechanical problems

We reformulate the density matrix renormalization group method (DMRG) in te rms of a single block, instead of the standard left and right blocks used i n the construction of the superblock. This version of the DMRG, which we ca ll the puncture renormalization group (PRG), makes easy and natural the ext ension of the DMRG to higher-dimensional lattices. To test numerically this proposal, we study several quantum mechanical models in one, two and three dimensions. In 1D the performance of the standard DMRG is much better than its PRG version, however, for 2D models the PRG is more efficient than the DMRG in a variety of circumstances. In 3D the PRG performs also quite well . (C) 2001 Elsevier Science B.V. All rights reserved.