Density matrix renormalization group in the discrete variable representation basis

TL;DR

This paper introduces a numerical implementation of the density matrix renormalization group (DMRG) method using the discrete variable representation (DVR) basis, simplifying integral calculations and effectively applied to a pseudo-hydrogen chain.

Contribution

The paper presents a novel DVR-based DMRG implementation that simplifies integral computations and demonstrates high accuracy in a one-dimensional hydrogen chain.

Findings

DMRG with DVR basis agrees with CASCI within 0.1 mEh

DVR basis simplifies one- and two-electron integral calculations

Effective application to a pseudo-hydrogen chain

Abstract

We present a numerical implementation of the density matrix renormalization group (DMRG) using the discrete variable representation (DVR) basis set. One main advantage of using the local DVR basis sets is that the computations of one-electron integral and two-electron repulsion integrals are drastically simplified. For comparison, we further implemented DVR complete active space configuration interaction (CASCI) using canonical molecular orbitals. These methods are applied to a one-dimensional pseudo-hydrogen chain under screened Coulomb potential. The DMRG ground state energy agrees with CASCI up to 0.1 mEh with a very small number of bond dimensions.