The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei

TL;DR

The paper reviews the In-Medium Similarity Renormalization Group (IM-SRG), a new ab initio method for nuclear structure, detailing its theoretical foundations, practical implementations, and comparisons with other many-body approaches.

Contribution

It provides a comprehensive overview of IM-SRG, including flow equations, generator choices, truncation strategies, and extensions to open-shell nuclei and operator evolution, advancing nuclear many-body theory.

Findings

IM-SRG effectively decouples ground states from excitations

Approximate center-of-mass factorization is achieved

Perturbative analysis clarifies IM-SRG's relation to other methods

Abstract

We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab inito method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell- model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.