Advanced density matrix renormalization group method for nuclear structure calculations

TL;DR

This paper introduces an advanced DMRG method with optimized orbital ordering and quantum information-based active space expansion, improving nuclear structure calculations and benchmarking results against established models.

Contribution

The paper presents a novel DMRG implementation incorporating orbital ordering and quantum information concepts, achieving accurate nuclear energy calculations and insights into orbital correlations.

Findings

Resolved a 400 keV discrepancy in $^{56}$Ni ground state energy.

First DMRG results for $^{64}$Ge in the $pf+g9/2$ shell model.

Identified correlation structures among proton and neutron orbitals.

Abstract

We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous $400$ KeV discrepancy in the ground state energy of $^{56}$Ni. We then report the first DMRG results in the $pf+g9/2$ shell model space for the ground $0^+$ and first $2^+$ states of $^{64}$Ge which are benchmarked with reference data obtained from Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of the two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.