Single-Block Renormalization Group: Quantum Mechanical Problems

Abstract

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.

RevTex4b4, 13 pages, two-column, 8 figs

References in corpus (4)

• Phase separation and stripe formation in the 2D t-J model: a comparison of numerical results
• Self-Consistent Tensor Product Variational Approximation for 3D Classical Models
• Kramers-Wannier Approximation for 3D Ising Model
• A Density Matrix Renormalization Group Approach to an Asymptotically Free Model with Bound States

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• Tensor Product State Formulation for the Spin 1/2 Antiferromagnetic XXZ Model on the Checkerboard Lattice
• Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube