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

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.

25 pages, 18 figures, minor typos corrected and references updated

References in corpus (5)

• Model-independent low momentum nucleon interaction from phase shift equivalence
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
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Cited by in corpus (12)

• Improved nuclear matter calculations from chiral low-momentum interactions
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
• Evolving Nuclear Many-Body Forces with the Similarity Renormalization Group
• Density Matrix Expansion for Low-Momentum Interactions
• Decoupling in the Similarity Renormalization Group for Nucleon-Nucleon Forces
• The Renormalization Group in Nuclear Physics
• Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Fixed points of the Similarity Renormalization Group and the Nuclear Many-Body Problem
• Similarity Renormalization Group for Few-Body Systems
• Light antiproton-nucleus systems at low energies with the ab initio NCSM/RGM method