The Density Matrix Renormalization Group and the Shell Model

TL;DR

This paper discusses adapting the Density Matrix Renormalization Group (DMRG) method for large-scale nuclear shell model calculations, introducing an angular-momentum conserving variant and demonstrating its efficiency and accuracy.

Contribution

The authors develop an angular-momentum conserving DMRG variant (JDMRG) tailored for nuclear physics and demonstrate its effectiveness in shell model calculations for nuclei.

Findings

High agreement with exact shell model results for $^{48}$Cr and $^{56}$Ni

Fraction of the full space needed decreases with increasing space size

JDMRG is a practical and efficient truncation strategy for nuclear shell models

Abstract

We summarize our recent efforts to develop the Density Matrix Renormalization Group (DMRG) method into a practical truncation strategy for large-scale nuclear shell model calculations. Following an overview of the essential features of the DMRG, we discuss the changes we have implemented for its use in nuclei. In particular, we have found it useful to develop an angular-momentum conserving variant of the method (the JDMRG). We then summarize the principal results we have obtained to date, first reporting test results for $^{48}$Cr and then more recent test results for $^{56}$Ni. In both cases we consider nucleons limited to the 2p-1f shell. While both calculations produce a high level of agreement with the exact shell model results, the fraction of the complete space required to achieve this high level of agreement is found to go down rapidly as the size of the full space grows.