In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

Abstract

We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory, Configuration-Interaction Monte Carlo, and the Self-Consistent Green's Function approach. The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.

arXiv comment73 pages, to appear in Lecture Notes in Physics (Springer), "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", edited by M. Hjorth-Jensen, M. P. Lombardo, and U. van Kolck

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Cited by in corpus (15)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Strangeness and $\Delta$ resonance in compact stars with relativistic-mean-field models
• Normal-ordered $k$-body approximation in particle-number-breaking theories
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• IMSRG with flowing 3 body operators, and approximations thereof
• Screening and anti-screening of the pairing interaction in low-density neutron matter
• Diagrammatic ab initio methods for infinite nuclear matter with modern chiral interactions
• Beta Decay in Medium-Mass Nuclei with the In-Medium Similarity Renormalization Group
• High-resolution momentum distributions from low-resolution wave functions
• Importance truncation in non-perturbative many-body techniques
• The quasi-deuteron model at low RG resolution
• Operator evolution from the similarity renormalization group and the Magnus expansion
• The "Folk Theorem" on Effective Field Theory: How Does It Fare in Nuclear Physics?