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The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei (1512.06956v1)

Published 22 Dec 2015 in nucl-th

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.

Citations (333)

Summary

  • The paper introduces a novel ab initio method that decouples nuclear ground states from excitations via continuous unitary transformations.
  • It details the use of distinct generator choices and truncation schemes, such as IM-SRG(2), to balance computational efficiency with accurate modeling of medium-mass nuclei.
  • Numerical results using softened chiral interactions validate the method’s convergence and highlight its potential to enhance theoretical nuclear structure studies.

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

The paper of the In-Medium Similarity Renormalization Group (IM-SRG) method provides an insightful advancement in the field of nuclear structure calculations. The paper presents a detailed review of the IM-SRG, exploring its capabilities as an ab initio approach for solving the nuclear many-body problem by decoupling the ground state from excitations via a continuous unitary transformation. This methodology is particularly significant for medium-mass nuclei where traditional ab initio methods face computational challenges.

Overview of IM-SRG

The IM-SRG employs flow equations to achieve a transformation of the many-body Hamiltonian, aiming for a desired decoupling, which simplifies the calculation of nuclear ground states and other properties. The essence of the method is to perform these transformations using a choice of generators that control the flow's properties and the resulting evolved Hamiltonian's suitability for further calculations. The primary focus lies on balancing accuracy and computational feasibility through systematic truncation, i.e., keeping only up to certain particle rank terms in the normal-ordered Hamiltonian.

Key Functionalities

  • Generator Choices: The paper examines different types of generators, such as White and Wegner types, each with distinct implications for decoupling efficiency and computational stability. The White generator, with its choice of using Epstein-Nesbet or M{\o}ller-Plesset denominators, offers computational efficiency but can be sensitive to small denominators. The Wegner generator, although inherently stable, can lead to increased computational demands.
  • Truncation Schemes: A focal point of the paper is the truncation at the normal-ordered two-body level (IM-SRG(2)), which retains computational manageability while providing an accurate approximation of nuclear properties. For a deeper insight, perturbative analyses are performed to ascertain the contributions of higher-order terms, offering guidance on improving truncation schemes.
  • Comparative Efficiency: Compared to other methods such as Coupled Cluster (CC) and many-body perturbation theory (MBPT), the IM-SRG shows competitive performance, especially in medium-mass nuclei, where it provides a good compromise between computational cost and physical accuracy.

Numerical Results and Computational Strategy

The authors provide extensive numerical results illustrating the convergence properties of the IM-SRG for different choices of generators and interactions. Notably, using softened chiral interaction potentials, the method achieves satisfactory convergence for ground-state energies across various nuclei, highlighting its viability for applications in nuclear physics. This is a testament to the method's robustness when handling full Hamiltonians that include nucleon-nucleon and three-nucleon interactions at varying resolution scales.

Theoretical Implications

The development of the IM-SRG method marks a significant step toward more accurate theoretical modeling of nuclear structure. By employing renormalization group techniques within the nuclear medium, the IM-SRG effectively manages strong nucleon-nucleon correlations, paving the way for applying this framework to a broader class of many-body systems. Furthermore, the ability to adapt the IM-SRG to include three-nucleon interactions nonperturbatively enhances its predictive power, making it a versatile tool that complements existing ab initio methods.

Future Directions

The adaptability of the IM-SRG encourages ongoing research to extend its applications, including its use in deriving effective interactions for the nuclear shell model in a nonperturbative manner. Future developments could further refine the method's accuracy and efficiency, potentially exploring multi-reference states and integrating with other computational approaches. Moreover, the consistent evolution of operators within the IM-SRG framework promises to improve calculations of observable properties, expanding its utility in theoretical nuclear physics and related disciplines.

Conclusion

In conclusion, the IM-SRG method represents a sophisticated approach to solving the complexities of nuclear structure by leveraging renormalization group concepts tailored for the nuclear medium. Its flexibility and computational efficiency make it a promising addition to the toolkit of nuclear physicists, with applications extending significantly beyond current horizons. As the method continues to evolve, it is anticipated to make impactful contributions to our understanding of nuclear matter and the fundamental interactions at play.

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