The Magnus expansion and the in-medium similarity renormalization group

Abstract

We present an improved variant of the in-medium similarity renormalization group (IM-SRG) based on the Magnus expansion. In the new formulation, one solves flow equations for the anti-hermitian operator that, upon exponentiation, yields the unitary transformation of the IM-SRG. The resulting flow equations can be solved using a first-order Euler method without any loss of accuracy, resulting in substantial memory savings and modest computational speedups. Since one obtains the unitary transformation directly, the transformation of additional operators beyond the Hamiltonian can be accomplished with little additional cost, in sharp contrast to the standard formulation of the IM-SRG. Ground state calculations of the homogeneous electron gas (HEG) and ${}^{16}$O nucleus are used as test beds to illustrate the efficacy of the Magnus expansion.

12 pages, 9 figures; fixed typos and added a reference

References in corpus (14)

• The Magnus expansion and some of its applications
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• In-Medium Similarity Renormalization Group for Nuclei
• Evolution of Nuclear Many-Body Forces with the Similarity Renormalization Group
• Coupled-cluster theory for three-body Hamiltonians
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
• In-Medium Similarity Renormalization Group for Open-Shell Nuclei
• Convergence in the no-core shell model with low-momentum two-nucleon interactions
• Ab Initio Multi-Reference In-Medium Similarity Renormalization Group Calculations of Even Calcium and Nickel Isotopes
• A driven similarity renormalization group approach to quantum many-body problems
• Solution of the center-of-mass problem in nuclear structure calculations
• Momentum space evolution of chiral three-nucleon forces
• Effects of three-nucleon forces and two-body currents on Gamow-Teller strengths
• From the lightest nuclei to the equation of state of asymmetric nuclear matter with realistic nuclear interactions

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