Analytic Formulations of the Density Matrix Renormalization Group

TL;DR

This paper introduces two new analytic formulations of the Density Matrix Renormalization Group method that combine block renormalization with variational and Fokker-Planck techniques to improve the computation of critical properties.

Contribution

It presents novel analytic formulations of DMRG that integrate BRG with variational and Fokker-Planck methods for enhanced accuracy.

Findings

Applied to the ITF model, achieving improved critical property calculations

Compared new methods with traditional BRG, showing better results

Validated approaches through numerical experiments

Abstract

We present two new analytic formulations of the Density Matrix Renormalization Group Method. In these formulations we combine the block renormalization group (BRG) procedure with Variational and Fokker-Planck methods. The BRG method is used to reduce the lattice size while the latter are used to construct approximate target states to compute the block density matrix. We apply our DMRG methods to the Ising Model in a transverse field (ITF model) and compute several of its critical properties which are then compared with the old BRG results.