The Density Matrix Renormalization Group for finite Fermi systems

TL;DR

This paper reviews the adaptation of the Density Matrix Renormalization Group method from one-dimensional quantum lattices to finite Fermi systems, highlighting recent developments and applications across various fields.

Contribution

It provides a comprehensive overview of modifications to DMRG for finite Fermi systems and discusses recent advancements including symmetry incorporation.

Findings

Successful application to quantum chemistry and nuclear systems

Enhanced algorithmic efficiency through symmetry integration

Broad applicability to two-dimensional electron systems

Abstract

The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of one-dimensional quantum lattices. The method, as originally introduced, was based on the iterative inclusion of sites on a real-space lattice. Based on its enormous success in that domain, it was subsequently proposed that the DMRG could be modified for use on finite Fermi systems, through the replacement of real-space lattice sites by an appropriately ordered set of single-particle levels. Since then, there has been an enormous amount of work on the subject, ranging from efforts to clarify the optimal means of implementing the algorithm to extensive applications in a variety of fields. In this article, we review these recent developments. Following a description of the real-space DMRG method, we discuss the key steps that were undertaken to modify it for use on finite Fermi systems and then describe its applications to Quantum Chemistry, ultrasmall superconducting grains, finite nuclei and two-dimensional electron systems. We also describe a recent development which permits symmetries to be taken into account consistently throughout the DMRG algorithm. We close with an outlook for future applications of the method.