Density Matrix Renormalization Group Lagrangians

TL;DR

This paper formulates a Lagrangian approach to the Density Matrix Renormalization Group (DMRG), enabling variational optimization of wavefunctions and paving the way for analytic response and derivative theories.

Contribution

It introduces a novel Lagrangian framework for DMRG that facilitates variational minimization and analytical developments in the method.

Findings

Lagrangians yield the optimal DMRG wavefunction variationally.

Analogies drawn between DMRG Lagrangians and Hartree-Fock expressions.

Framework will aid in developing response and derivative theories for DMRG.

Abstract

We introduce a Lagrangian formulation of the Density Matrix Renormalization Group (DMRG). We present Lagrangians which when minimised yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz, as well as within the canonical form of the matrix product that is constructed within the DMRG sweep algorithm. Some of the results obtained are similar to elementary expressions in Hartree-Fock theory, and we draw attention to such analogies. The Lagrangians introduced here will be useful in developing theories of analytic response and derivatives in the DMRG.