Local Projections of Low-Momentum Potentials

TL;DR

This paper introduces a method called local projections to transform evolved nuclear interactions into a form that is more intuitive and easier to use, by separating local and non-local components after renormalization group evolution.

Contribution

The paper presents a novel local projection technique that simplifies low-momentum nuclear potentials by isolating local interactions, aiding intuition and computational methods.

Findings

Local projections effectively separate local and non-local parts of evolved potentials.

Residual interactions after projection are weak and suitable for perturbative approaches.

Flow towards universal low-momentum interactions is observed after SRG evolution.

Abstract

Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment.