Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model

Abstract

A one-dimensional system of bosons with short-range repulsion and mid-range attraction is used as a laboratory to explore the evolution of many-body forces by the Similarity Renormalization Group (SRG). The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. This approach, which can be directly generalized to three-dimensional nuclei, is fully unitary up to induced A-body forces when applied with an A-particle basis (e.g., A-body bound-state energies are exactly preserved). The oscillator matrix elements for a given A can then be used in larger systems. Errors from omitted induced many-body forces show a hierarchy of decreasing contribution to binding energies. An analysis of individual contributions to the growth of many-body forces demonstrates such a hierarchy and provides an understanding of its origins.

23 pages, 11 figures, Changed section on analysis of three-body running

References in corpus (11)

• Three-Nucleon Forces from Chiral Effective Field Theory
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Few-nucleon systems in translationally invariant harmonic oscillator basis
• Convergence in the no-core shell model with low-momentum two-nucleon interactions
• Solution of few-body problems with the stochastic variational method: I. Central forces
• Shell-model calculations for the three-nucleon system
• Four-nucleon shell-model calculations in a Faddeev-like approach
• Block Diagonalization using SRG Flow Equations
• Are low-energy nuclear observables sensitive to high-energy phase shifts?
• Decoupling in the Similarity Renormalization Group for Nucleon-Nucleon Forces
• Three-Body Forces Produced by a Similarity Renormalization Group Transformation in a Simple Model

Cited by in corpus (20)

• Modern Theory of Nuclear Forces
• Recent developments in no-core shell-model calculations
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• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
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• P-shell nuclei using Similarity Renormalization Group evolved three-nucleon interactions
• Operator Evolution via the Similarity Renormalization Group I: The Deuteron
• Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
• The Renormalization Group in Nuclear Physics
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• Symmetries of the Similarity Renormalization Group for Nuclear Forces
• Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study
• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo
• The Similarity Renormalization Group with Novel Generators
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• The Similarity Renormalization Group for Three-Body Interactions in One Dimension
• Implicit and explicit renormalization: two complementary views of effective interactions
• Renormalization group evolution of optical potentials: explorations using a toy model
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Nuclei and chiral dynamics