Operator Evolution via the Similarity Renormalization Group I: The Deuteron

Abstract

Similarity Renormalization Group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this paper on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.

33 pages, 19 figures. Improved figures 17 and 18. Expanded comments on OPE in text

References in corpus (14)

• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Dispersion analysis of the nucleon form factors including meson continua
• Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
• Recent observation of short range nucleon correlations in nuclei and their implications for the structure of nuclei and neutron stars
• Convergence in the no-core shell model with low-momentum two-nucleon interactions
• Low-momentum interactions with smooth cutoffs
• Block Diagonalization using SRG Flow Equations
• Are low-energy nuclear observables sensitive to high-energy phase shifts?
• Chiral effective theory predictions for deuteron form factor ratios at low Q^2
• Decoupling in the Similarity Renormalization Group for Nucleon-Nucleon Forces
• Deuteron form factors in chiral effective theory: regulator-independent results and the role of two-pion exchange
• Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
• Variational Calculations using Low-Momentum Potentials with Smooth Cutoffs

Cited by in corpus (4)

• Evolving Nuclear Many-Body Forces with the Similarity Renormalization Group
• Nucleon momentum distributions, their spin-isospin dependence and short-range correlations
• Quasiparticle Random Phase Approximation with Interactions from the Similarity Renormalization Group
• Tan contact and universal high momentum behavior of the fermion propagator in the BCS-BEC crossover