The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

H. Hergert; S. K. Bogner; T. D. Morris; A. Schwenk; K. Tsukiyama

doi:10.1016/j.physrep.2015.12.007

The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, K. Tsukiyama

Research output: Contribution to journal › Review article › peer-review

305 Scopus citations

Abstract

We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio 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.

Original language	English
Pages (from-to)	165-222
Number of pages	58
Journal	Physics Reports
Volume	621
DOIs	https://doi.org/10.1016/j.physrep.2015.12.007
State	Published - Mar 21 2016
Externally published	Yes

Funding

We thank C. Barbieri, S. Binder, A. Calci, T. Duguet, J. Engel, F. Evangelista, R. J. Furnstahl, G. Hagen, K. Hebeler, M. Hjorth-Jensen, J. D. Holt, J. Langhammer, J. Menéndez, T. Otsuka, T. Papenbrock, R. Roth, J. Simonis, V. Somà and S. R. Stroberg for useful discussions on the topics of this review. This work was supported in part by the NUCLEI SciDAC Collaboration under the U.S. Department of Energy Grant Nos. DE-SC0008533 and DE-SC0008511 , the National Science Foundation under Grant Nos. PHY-1002478 , PHY-1306250 , PHY-1068648 and PHY-1404159 , the European Research Council Grant No. 307986 STRONGINT, the BMBF under Contract Nos. 06DA70471 and 05P15RDFN1 , and the Deutsche Forschungsgemeinschaft (DFG) through Grant SFB 634 . Computing resources were provided by the Ohio Supercomputing Center (OSC), and the Michigan State University High Performance Computing Center (HPCC)/Institute for Cyber-Enabled Research (iCER).

Funders	Funder number
NUCLEI
National Science Foundation	1002478, PHY-1068648, 1306250, 1068648, 1404159, 307986, PHY-1404159, PHY-1306250, PHY-1002478
U.S. Department of Energy	DE-SC0008511, DE-SC0008533
European Research Council
Deutsche Forschungsgemeinschaft	SFB 634
Bundesministerium für Bildung und Forschung	06DA70471, 05P15RDFN1

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10.1016/j.physrep.2015.12.007

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title = "The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei",

abstract = "We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio 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.",

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AU - Tsukiyama, K.

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N2 - We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio 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.

AB - We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio 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.

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The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

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