Nuclear Structure from the In-Medium Similarity Renormalization Group

Abstract

Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, and multiple approximate, computationally efficient many-body methods have been developed that can be routinely applied for medium-mass nuclei. This has made it possible to confront modern nuclear interactions from Chiral Effective Field Theory, that are rooted in Quantum Chromodynamics with a wealth of experimental data. Here, we discuss one of these efficient new many-body methods, the In-Medium Similarity Renormalization Group (IMSRG), and its applications in modern nuclear structure theory. The IMSRG evolves the nuclear many-body Hamiltonian in second-quantized form through continuous unitary transformations that can be implemented with polynomial computational effort. Through suitably chosen generators, we drive the matrix representation of the Hamiltonian in configuration space to specific shapes, e.g., to implement a decoupling of low- and high-energy scales, or to extract energy eigenvalues for a given nucleus. We present selected results from Multireference IMSRG (MR-IMSRG) calculations of open-shell nuclei, as well as proof-of-principle applications for intrinsically deformed medium-mass nuclei. We discuss the successes and prospects of merging the (MR-)IMSRG with many-body methods ranging from Configuration Interaction to the Density Matrix Renormalization Group, with the goal of achieving an efficient simultaneous description of dynamic and static correlations in atomic nuclei.

Invited contribution presented by H. H. at the 19th International Conference on Recent Progress in Many-Body Theories, June 25-30, 2017, APCTP, Pohang, Korea. Extended version: 30 pages, 14 figures

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Cited by in corpus (14)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• In-medium similarity renormalization group with three-body operators
• Generator-coordinate reference states for spectra and $0\nu \beta \beta$ decay in the in-medium similarity renormalization group
• Shell evolution of $N=40$ isotones towards ${}^{60}$Ca: First spectroscopy of ${}^{62}$Ti
• Ab initio uncertainty quantification of neutrinoless double-beta decay in ${}^{76}$Ge
• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
• Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Benchmark neutrinoless double-beta decay matrix elements in a light nucleus
• Uncertainty quantification in nuclear shell model
• Precision measurement of the $E2$ transition strength to the 2${}_1^{+}$ state of ${}^{12}$C
• Microscopically based energy density functionals for nuclei using the density matrix expansion