Operator evolution from the similarity renormalization group and the Magnus expansion

“…These quantities, which can be dramatically different from model to model -as has been known for decades -are not observable. The SRC probabilities and highmomentum distributions in nuclei, which have been and are being extracted from hard electron scattering experiments [64][65][66][67][68][69][70][71][72][73][74][75][76] are equally non-observable, although highmomentum information can be extracted from data in a scale and scheme dependent way [93]. The recent comprehensive analysis from Ref.…”

Section: Short-range Correlationsmentioning

confidence: 99%

“…The recent comprehensive analysis from Ref. [93] describes the situation very clearly: the SRC knock-out experiments do have merit, but their value "...is not new insight into the interaction, but to demonstrate that short-range physics can be isolated and to a certain extent controlled." Results of these experiments cannot be used to to select the "best" off-shell behavior, a concept that can be proven to be fundamentally impossible [94][95][96].…”

Section: Short-range Correlationsmentioning

confidence: 99%

“…If predictions with a particular potential are closest to the knock-out measurements, in no way that implies that the "measured" off-shell behavior has selected that particular interaction -it means that the latter is more suitable for the assumptions made in the data analyses, for instance, impulse approximation. Ultimately, predictions from observables must agree for any realistic model, whether SRC are built into the wave function or in the operators [93].…”

Section: Short-range Correlationsmentioning

confidence: 99%

See 1 more Smart Citation

An overview of symmetric nuclear matter properties from chiral interactions up to fourth order of the chiral expansion

Sammarruca,

Millerson

2021

Preprint

View full text Add to dashboard Cite

We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at N 3 LO and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.

show abstract

“…The (free-space) SRG is a continuous unitary transformation that is designed to decouple the low and highmomentum components of the Hamiltonian and other observables of interest (see, e.g., [39,40]). The transformation, or SRG flow, is parameterized with a continuous flow parameter s, and implemented through the operator flow equation…”

Section: A Singular Value Decompositionmentioning

confidence: 99%

Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions

Zhu,

Wirth,

Hergert

2021

Preprint

View full text Add to dashboard Cite

One of the main challenges for ab initio nuclear many-body theory in the coming decade is the growth of computational and storage costs as calculations are extended to increasingly heavy, exotic, and structurally complex nuclei. Here, we investigate the factorization of nuclear interactions as a means to address this issue. We perform Singular Value Decompositions of current nucleon-nucleon interactions in partial wave representation and study the dependence of the singular value spectrum on interaction characteristics like regularization schemes and resolution scales.Next, we develop and implement the Similarity Renormalization Group (SRG) evolution of the interaction in terms of the relevant singular vectors, and demonstrate that this SVD-SRG approach accurately preserves two-nucleon observables.We find that low-resolution interactions naturally allow the truncation of the SVD at low rank, and that a small number of relevant components is sufficient to capture the nuclear interaction and perform an accurate SRG evolution, while the Coulomb interaction requires special consideration. The rank is uniform across all partial waves and almost independent of the basis choice in the tested cases. This suggests an interpretation of the relevant singular components as mere representations of a small set of abstract operators that can describe the interaction and its SRG flow.Following the traditional workflow for nuclear interactions, we discuss how the transformation between the center-of-mass and laboratory frames creates redundant copies of the partial wave components when implemented in matrix representation, and we discuss strategies for mitigation.Finally, we test the low-rank approximation to the SRG-evolved interactions in many-body calculations using the In-Medium SRG. By including nuclear radii in our analysis, we verify that the implementation of the SRG using the singular vectors of the interaction does not spoil the evolution of other observables.

show abstract

Operator evolution from the similarity renormalization group and the Magnus expansion

Cited by 12 publications

References 52 publications

Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group

Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group

An overview of symmetric nuclear matter properties from chiral interactions up to fourth order of the chiral expansion

Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions

Contact Info

Product

Resources

About