Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains

TL;DR

This paper demonstrates the equivalence between the variational matrix product method and the density matrix renormalization group for spin chains, introducing a rotationally invariant approach that enhances parameter handling and computes key physical properties.

Contribution

It introduces a rotationally invariant matrix product method and establishes its relation to DMRG, enabling larger parameter spaces and improved analysis of isotropic spin chains.

Findings

Computed ground state energy density of spin 1 Heisenberg chain.

Determined spin correlation length using the new method.

Showed the equivalence between MPM and DMRG methods.

Abstract

We present a rotationally invariant matrix product method (MPM) of isotropic spin chains. This allows us to deal with a larger number of variational MPM parameters than those considered earlier by other authors. We also show the relation between the MPM and the DMRG method of White. In our approach the eigenstates of the density matrix associated with the MPM are used as variational parameters together with the standard MPM parameters. We compute the ground state energy density and the spin correlation length of the spin 1 Heisenberg chain.