Tracing the evolution of nuclear forces under the similarity renormalization group

TL;DR

This paper investigates how the similarity renormalization group (SRG) transforms nuclear forces, revealing that SRG primarily shifts diagonal matrix elements downward, which explains its effectiveness in simplifying nuclear interactions.

Contribution

It provides a novel trace-based analysis of SRG evolution, offering a complementary perspective to the common 'softening' interpretation and clarifying the primary effects on the Hamiltonian.

Findings

SRG shifts diagonal matrix elements downward

Off-diagonal elements change minimally during SRG evolution

Trace analysis explains SRG's success in simplifying nuclear forces

Abstract

I examine the evolution of nuclear forces under the similarity renormalization group (SRG) using traces of the many-body configuration-space Hamiltonian. While SRG is often said to "soften" the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly smaller changes. By employing traces, I argue that this is a very natural outcome as one diagonalizes a matrix, and helps one to understand the success of SRG.