Single-Block Renormalization Group: Quantum Mechanical Problems

Details Single-Block Renormalization Group: Quantum Mechanical Problems Single-Block Renormalization Group: Quantum Mechanical Problems

2000-09-29

arxiv.org/abs/cond-mat/0009474v1

Physics

Condensed Matter

RevTex4b4, 13 pages, two-column, 8 figs

Scientific paper

10.1016/S0550-3213(01)00073-6

We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture renormalization group (PRG), makes easy and natural the extension 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.

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