Two-particle irreducible functional renormalization group schemes---a comparative study

Abstract

We derive functional renormalization group schemes for Fermi systems which are based on the two-particle irreducible approach to the quantum many-body problem. In a first step, the cutoff is introduced in the non-interacting propagator as it is commonly done in functional renormalization group based on one-particle irreducible vertex functions. The most natural truncation of the resulting infinite hierarchy of flow equations is shown to be fully equivalent to self-consistent perturbation theory. An earlier suggested alternative truncation strategy is considered as well. In a second step, the cutoff is introduced in the two-particle interaction. Again two truncation procedures are investigated, one of which was derived before. In the latter, the mean-field solution of the many-body problem is considered as the starting point of the renormalization group flow. We compare the performance and the required numerical resources for solving the coupled flow equations for all the approximate schemes by applying them to the problem of the quantum anharmonic oscillator. In a functional integral representation, this model has a formal similarity to the quantum many-body problem. The perspectives for applying the derived two-particle irreducible functional renormalization group approaches to zero- and one-dimensional systems of correlated fermions are discussed.

32 pages, 6 figures (9 plots)

References in corpus (47)

• Aspects of the Functional Renormalisation Group
• Functional renormalization group approach to correlated fermion systems
• Introduction to the functional RG and applications to gauge theories
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Renormalization Flow of Bound States
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• On the fulfillment of Ward identities in the functional renormalization group approach
• Nonequilibrium functional renormalization group for interacting quantum systems
• From infinite to two dimensions through the functional renormalization group
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Functional renormalization for spontaneous symmetry breaking in the Hubbard model
• Nonequilibrium functional RG with frequency dependent vertex function: A study of the single impurity Anderson model
• Functional renormalization group for non-equilibrium quantum many-body problems
• Renormalization group flows into phases with broken symmetry
• A finite-frequency functional RG approach to the single impurity Anderson model
• A novel approach to transport through correlated quantum dots
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Flow Equations for the BCS-BEC Crossover
• Interaction flow method for many-fermion systems
• A renormalization group approach to time dependent transport through correlated quantum dots
• Functional renormalization group approach to zero-dimensional interacting systems
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Superconductivity in the two-dimensional $t$-$t^{\prime }$-Hubbard model
• Pairing in Many-Fermion Systems: An Exact Renormalisation Group Treatment
• Functional renormalization group study of the interacting resonant level model in and out of equilibrium
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Effective action and density functional theory
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Correlated starting points for the functional renormalization group
• Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Properties of multi-particle Green and vertex functions within Keldysh formalism
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Effective interactions and fluctuation effects in spin-singlet superfluids
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• Bosonic effective action for interacting fermions
• Nonperturbative renormalization-group approach to fermion systems in the two-particle-irreducible effective action formalism
• Solution of the Anderson impurity model via the functional renormalization group
• Functional renormalization group for quantized anharmonic oscillator
• An alternative functional renormalization group approach to the single impurity Anderson model
• Non-Perturbative Renormalization Group Analysis in Quantum Mechanics
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
• Schwinger-Dyson Renormalization Group
• Towards Density Functional Calculations from Nuclear Forces
• Renormalization, Conservation Laws and Transport in Correlated Electron Systems

Cited by in corpus (23)

• The nonperturbative functional renormalization group and its applications
• Real time correlation functions and the functional renormalisation group
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Functional Renormalization Group and Kohn-Sham scheme in Density Functional Theory
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Functional renormalization group and 2PI effective action formalism
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Emergent Hadrons and Diquarks
• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study
• 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
• Renormalization group flow of the Luttinger-Ward functional: conserving approximations and application to the Anderson impurity model
• Fermi-edge singularity and the functional renormalization group
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• Master equation based steady-state cluster perturbation theory
• Review of recent developments of the functional renormalization group for systems out of equilibrium
• Construction of energy density functional for arbitrary spin polarization using functional renormalization group
• Physics-informed neural networks for solving functional renormalization group on a lattice
• 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
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions