Symmetries of the similarity renormalization group for nuclear forces

Timóteo, V. S.; Szpigel, S.; Arriola, E. Ruiz

doi:10.1103/physrevc.86.034002

Cited by 23 publications

(35 citation statements)

References 49 publications

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“…On a more fundamental level, recent lattice calculations have observed Wigner's symmetry at the potential level [11] and also at the scattering length level for the unphysical pion masses about four times larger than in the real world [12]. In the present contribution we summarize the findings of our renalysis [13] based on the Similarity Renormalization Group and provide some outlook.…”

Section: Introductionmentioning

confidence: 86%

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Nuclear Symmetries and the Similarity Renormalization Group

Arriola¹,

Szpigel²,

Timóteo³

2013

Proceedings of the 7th International Workshop on Chiral Dynamics — PoS(CD12)

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We review the role played by long-distance symmetries within the context of the similarity renormalization group (SRG) approach. This is based on phase-shift-preserving continuous unitary transformations that evolve Hamiltonians with a cutoff on energy differences. We find that there is a SRG cutoff, λ Wigner ∼ 3fm −1 for which almost perfect fulfillment of Wigner SU(4) symmetry is found at the two body level. This suggests to look for similar symmetry patterns for three-and four-body forces. We also analyze the impact of potentials based on Chiral Perturbation Theory in Nuclear Structure calculations.

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Section: Introductionmentioning

confidence: 86%

“…The solution generates from an initial potential V λ =∞ (p , p) a oneparameter family of phase-equivalent potentials at all energies, δ λ (p) = δ λ =∞ (p) which are driven to a stable fixed point at λ → 0 [13]. Large momentum-differences |p − p | λ are suppressed as…”

Section: Wigner Symmetry and The Srgmentioning

confidence: 99%

Nuclear Symmetries and the Similarity Renormalization Group

Arriola¹,

Szpigel²,

Timóteo³

2013

Proceedings of the 7th International Workshop on Chiral Dynamics — PoS(CD12)

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“…The similarity renormalization group (SRG) approach, developed by Glazek and Wilson [1,2] and independently by Wegner [3], has been intensively applied in the context of nuclear physics to handle multi-nucleon forces in order to soften the short-distance core [5,8] with a rather universal pattern for nuclear symmetries [21,38] and interactions [39]. The basic strategy underlying the application of the SRG methods to nuclear forces is to evolve an initial (bare) interaction H, which has been fitted to NN scattering data, via a continuous unitary transformation that runs a cutoff λ on energy differences.…”

Section: Srg Flow Equations In Operator Formmentioning

confidence: 99%

Fixed points of the SRG evolution and the on-shell limit of the nuclear force

2016

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We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff λ → 0 may be obtained from the eigenvalues of the hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit λ → 0 on a finite momentum grid. Another issue we investigate is the location on the diagonal of the hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of A = 2, 3, 4 systems are investigated and related to the ocurrence of a Tjon-line which emerges as the minimum of an avoided crossing between E α = 4E t − 3E d and E α = 2E t . All infrared features of the flow equations are illustrated using the toy model for the two-nucleon S -waves.

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“…• The role of long-distance symmetries within the context of SRG evolution has been explored recently [106]. A particular SRG resolution scale is identified for which the Wigner SU(4) symmetry is almost perfectly realized at the two-body level.…”

Section: Other Applications and Future Directionsmentioning

confidence: 99%

New applications of renormalization group methods in nuclear physics

2013

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Abstract. We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

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Symmetries of the similarity renormalization group for nuclear forces

Cited by 23 publications

References 49 publications

Nuclear Symmetries and the Similarity Renormalization Group

Nuclear Symmetries and the Similarity Renormalization Group

Fixed points of the SRG evolution and the on-shell limit of the nuclear force

New applications of renormalization group methods in nuclear physics

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