Operator Evolution via the Similarity Renormalization Group I: The Deuteron

TL;DR

This paper investigates the properties of SRG-evolved operators, demonstrating their advantages in simplifying nuclear calculations for the deuteron and potentially for other few-body systems, while addressing practical approximation concerns.

Contribution

It provides an analysis of SRG-evolved operators' properties, highlighting simplifications and their implications for nuclear structure calculations.

Findings

SRG-evolved operators retain advantageous features.

Factorization leads to additional simplifications.

Applicability to few-body systems is promising.

Abstract

Similarity Renormalization Group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this paper on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.