Decoupling of Spurious Deep Bound States with the Similarity Renormalization Group

Abstract

The Similarity Renormalization Group (SRG) is a continuous series of unitary transformations that can be implemented as a flow equation. When the relative kinetic energy ($\Trel$) is used in the SRG generator, nuclear structure calculations have shown greatly improved convergence with basis size because of the decoupling of high-energy and low-energy physics. However this generator can sometimes be problematic. A test case is provided by a study of initial interactions from chiral effective field theories with large cutoffs, which can lead to spurious deep bound states. We would like the SRG to decouple these from the physical shallow bound states. However, with $\Trel$ the high- and low-energy bound states are not decoupled in the usual sense. Replacing $\Trel$ by the momentum-space diagonal of the Hamiltonian ($H_d$) in the SRG generator does produce decoupling, such that the shallow states are in the low-momentum region and the deep bound states are at higher momentum. The flow toward universal low-momentum interactions is also restored.

10 pages, 18 figures

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Cited by in corpus (15)

• New applications of renormalization group methods in nuclear physics
• Correlated Fermion Pairs in Nuclei and Ultracold Atomic Gases
• The Renormalization Group in Nuclear Physics
• In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
• Symmetries of the Similarity Renormalization Group for Nuclear Forces
• Similarity Renormalization Group Evolution of Three-Nucleon Forces in a Hyperspherical Momentum Representation
• The Similarity Renormalization Group with Novel Generators
• Local Projections of Low-Momentum Potentials
• Universality in Similarity Renormalization Group Evolved Potential Matrix Elements and T-Matrix Equivalence
• Operator evolution from the similarity renormalization group and the Magnus expansion
• Alternative similarity renormalization group generators in nuclear structure calculations
• The Similarity Renormalization Group for Three-Body Interactions in One Dimension
• The infrared limit of the Similarity Renormalization Group evolution and Levinson's theorem
• Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory
• Fixed points of the SRG evolution and the on-shell limit of the nuclear force