Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory

Abstract

The present paper is the second of a series of publications that aim at investigating relevant directions to turn the nuclear energy density functional (EDF) method as an effective field theory (EFT). The EDF approach has known numerous successes in nuclear theory over the past decades and is currently the only microscopic technique that can be applied to all atomic nuclei. However, the phenomenological character of the EDF method also comes with important limitations, such as the lack of an explicit connection with quantum chromodynamics (QCD). As was argued in the first paper of this series, reformulating the EDF framework as an EFT would enable us to overcome these limitations. In particular, path-integral (PI) techniques are suited to achieve such a purpose as they allow to design numerous non-perturbative approximations and can take Lagrangians possibly derived from EFTs of QCD as inputs. In our previous paper, we have illustrated such technical features for diagrammatic PI techniques in a study of the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory. In the present work, we consider another class of PI techniques, i.e. functional renormalization group (FRG) approaches, that we apply to the same toy model. Despite our explicit interest for the nuclear many-body problem, the presented study is also directed towards FRG practitioners from various fields: technical details are provided for FRG techniques based on 1-particle-irreducible (1PI), 2-particle-irreducible (2PI) and 2-particle-point-irreducible (2PPI) effective actions (EAs), coined respectively as 1PI-, 2PI- and 2PPI-FRGs, and the treatment of the $O(N)$ symmetry is also addressed thoroughly. Connections between these various FRG methods are identified as well.

This article is part of a PhD project. The corresponding manuscript can be found at: arXiv:2210.16676

References in corpus (51)

• Exact evolution equation for the effective potential
• Introduction to Effective Field Theory
• Chiral symmetry breaking in continuum QCD
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Nonthermal fixed points and the functional renormalization group
• Ising exponents from the functional renormalisation group
• Exact flow equation for composite operators
• The local potential approximation in quantum gravity
• Functional renormalisation group approach to far-from-equilibrium quantum field dynamics
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Interaction flow method for many-fermion systems
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Functional renormalization group studies of nuclear and neutron matter
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Correlated starting points for the functional renormalization group
• Renormalization group methods and the 2PI effective action
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• Functional renormalization group approach to the Anderson impurity model
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• The Kinetic Energy Density in Kohn-Sham Density Functional Theory
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Non-perturbative predictions for cold atom Bose gases with tunable interactions
• Two-particle irreducible functional renormalization group schemes---a comparative study
• Effective Field Theory for Dilute Fermions with Pairing
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Multiloop flow equations for single-boson exchange fRG
• Modern theory of nuclear forces
• Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• Functional renormalization group for d-wave superconductivity in Hubbard type models
• Functional renormalization group approach to the Ising-nematic quantum critical point of two-dimensional metals
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• On the 2-point function of the O(N) model
• Generation of d-wave coupling in the two-dimensional Hubbard model from functional renormalization
• Functional renormalization group for quantized anharmonic oscillator
• Non-perturbative renormalization-group approach to lattice models
• Nuclear Structure at the Crossroads
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory
• Bosonic fluctuations in the $(1+1)$-dimensional Gross-Neveu(-Yukawa) model at varying $\mu$ and $T$ and finite $N$
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory

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