Three-Body Forces Produced by a Similarity Renormalization Group Transformation in a Simple Model

TL;DR

This paper demonstrates how a simple unitary renormalization group transformation can systematically produce and evolve two- and three-body interactions towards a band-diagonal form, simplifying many-body nuclear calculations.

Contribution

It introduces a diagrammatic approach to consistently evolve two- and three-body interactions in a simple model, applicable to realistic nuclear problems.

Findings

Transformations produce decoupling of low- and high-energy states.

Three-body interactions are consistently evolved alongside two-body interactions.

The approach simplifies many-body nuclear calculations.

Abstract

A simple class of unitary renormalization group transformations that force hamiltonians towards a band-diagonal form produce few-body interactions in which low- and high-energy states are decoupled, which can greatly simplify many-body calculations. One such transformation has been applied to phenomenological and effective field theory nucleon-nucleon interactions with success, but further progress requires consistent treatment of at least the three-nucleon interaction. In this paper we demonstrate in an extremely simple model how these renormalization group transformations consistently evolve two- and three-body interactions towards band-diagonal form, and introduce a diagrammatic approach that generalizes to the realistic nuclear problem.