Similarity renormalization group with novel generators

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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“…Recently, alternative generators that allow computationally much faster evolution have been explored, see Ref. [22] for details.…”

Section: Rg Evolution Of Nucleon-nucleon Interactionsmentioning

confidence: 99%

New applications of renormalization group methods in nuclear physics

2013

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“…This drives the Hamiltonian towards diagonal form in momentum space, thus weakening the coupling between low-and highmomentum states, though other generators have also been successful [26]. Rather than use the flow parameter, s, it is common to use λ = s −1/4 , to keep track of the sequence of Hamiltonians [19]; note that as λ decreases, the Hamiltonian will undergo more evolution.…”

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confidence: 99%

Operator evolution forab initiotheory of light nuclei

et al. 2014

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The past two decades have seen a revolution in ab initio calculations of nuclear properties. One key element has been the development of a rigorous effective interaction theory, applying unitary transformations to soften the nuclear Hamiltonian and hence accelerate the convergence as a function of the model space size. For consistency, however, one ought to apply the same transformation to other operators when calculating transitions and mean values from the eigenstates of the renormalized Hamiltonian. Working in a translationally-invariant harmonic oscillator basis for the twoand three-nucleon systems, we evolve the Hamiltonian, square-radius and total dipole strength operators by the similarity renormalization group (SRG). The inclusion of up to three-body matrix elements in the 4 He nucleus all but completely restores the invariance of the expectation values under the transformation. We also consider a Gaussian operator with adjustable range and find at short ranges an increased contribution from such induced three-body terms. . Of particular importance is the need to include ab initio three-body forces, for example, in correctly describing nuclear binding energies and spectra, especially the ground state spin of p-shell nuclei [5], the lifetime of 14 C [3], and the location of the neutron drip line for oxygen isotopes [6].These breakthrough discoveries have been driven by advances in computing, in effective field theory [7][8][9][10], in techniques for the solution of the nuclear many-body problem, such as the no-core shell model (NCSM) [11][12][13], and in modern effective interaction theory [14,15]. The latter takes the form of unitary transformations chosen to reduce the coupling between low-and highmomentum states, which arises from the bare nuclear interaction's "hard core" and leads to slow convergence in the size of the model space.Here we focus on the similarity renormalization group (SRG) [16,17], which has been successful when computing nuclear properties for a variety of nuclei [14,15,[18][19][20][21][22][23]. Independently developed by Glazek and Wilson [24] and Wegner [25], the SRG is a series of unitary transformations on the Hamiltonian,whereÛ s labels the sequence of transformations starting with the initial Hamiltonian at s = 0. This can be rewritten as a flow equation in s and an antihermitian generator,The generator is commonly chosen to be [T ,Ĥ s ], wherê T is the kinetic energy operator. This drives the Hamiltonian towards diagonal form in momentum space, thus weakening the coupling between low-and highmomentum states, though other generators have also been successful [26]. Rather than use the flow parameter, s, it is common to use λ = s −1/4 , to keep track of the sequence of Hamiltonians [19]; note that as λ decreases, the Hamiltonian will undergo more evolution.While formally the transformed Hamiltonian should be independent of the unitary transformation and specifically of the SRG flow parameter, the evolution induces higher-order terms, up to A-body, into the Hamiltonian. Previous ...

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“…The T rel -SRG flow of two-nucleon forces (2NF) has been studied in detail using both momentum representation [1,[4][5][6][7] and in a discrete harmonic oscillator (HO) basis [8].…”

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Similarity renormalization group evolution of three-nucleon forces in a hyperspherical momentum representation

Wendt

2013

Phys. Rev. C

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A new framework for computing the Similarity Renormalization Group (SRG) evolution of threenucleon forces (3NF) in momentum representation is presented. The use of antisymmetric threeparticle hyperspherical momentum states ensures unitary evolutions within certain basis truncations, much like antisymmetric harmonic oscillator SRG evolutions. Additionally, in each partial wave the T rel -SRG regulator is exactly represented, similar to recent 3NF momentum representation evolutions. Unitary equivalence is demonstrated for the triton using several chiral two-plus threenucleon interactions. This method allows for a clean visualization of the evolution of the threenucleon forces, which manifests the SRG decoupling pattern and low-momentum universality.

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Similarity renormalization group with novel generators

Cited by 28 publications

References 21 publications

New applications of renormalization group methods in nuclear physics

New applications of renormalization group methods in nuclear physics

Operator evolution forab initiotheory of light nuclei

Similarity renormalization group evolution of three-nucleon forces in a hyperspherical momentum representation

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