Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions

Abstract

We present a functional renormalization group (fRG) study of the two dimensional Hubbard model, performed with an algorithmic implementation which lifts some of the common approximations made in fRG calculations. In particular, in our fRG flow; (i) we take explicitly into account the momentum and the frequency dependence of the vertex functions; (ii) we include the feedback effect of the self-energy; (iii) we implement the recently introduced multiloop extension which allows us to sum up {\emph{all}} the diagrams of the parquet approximation with their exact weight. Due to its iterative structure based on successive one-loop computations, the loop convergence of the fRG results can be obtained with an affordable numerical effort. In particular, focusing on the analysis of the physical response functions, we show that the results become {\emph{independent}} from the chosen cutoff scheme and from the way the fRG susceptibilities are computed, i.e., either through flowing couplings to external fields, or through a "post-processing" contraction of the interaction vertex at the end of the flow. The presented substantial refinement of fRG-based computation schemes paves a promising route towards future quantitative fRG analyses of more challenging systems and/or parameter regimes.

53 pages, 19 figures

References in corpus (72)

• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Exact evolution equation for the effective potential
• Quantum Cluster Theories
• Functional renormalization group approach to correlated fermion systems
• Competing electronic orders on Kagome lattices at van Hove filling
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Renormalization group analysis of the 2D Hubbard model
• Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping
• Functional Renormalization Group for multi-orbital Fermi Surface Instabilities
• Local Electronic Correlation at the Two-Particle Level
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• Fate of the false Mott-Hubbard transition in two dimensions
• On the fulfillment of Ward identities in the functional renormalization group approach
• Mott physics and spin fluctuations: a unified framework
• From infinite to two dimensions through the functional renormalization group
• Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• Renormalization group flows into phases with broken symmetry
• A finite-frequency functional RG approach to the single impurity Anderson model
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• Theory of single-particle properties of the Hubbard model
• High-performance functional renormalization group calculations for interacting fermions
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Multiloop functional renormalization group for general models
• Multiloop functional renormalization group that sums up all parquet diagrams
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Instabilities of interacting electrons on the honeycomb bilayer
• Interaction flow method for many-fermion systems
• Quasiparticle anisotropy and pseudogap formation from the weak-coupling renormalization group point of view
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• Functional renormalization group for Luttinger liquids with impurities
• 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
• Parquet approximation for the 4x4 Hubbard cluster
• Parquet decomposition calculations of the electronic self-energy
• Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling
• Electron-doping versus hole-doping in the 2D t-t' Hubbard model
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Flow of the quasiparticle weight in the N-patch renormalization group scheme
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Quantum criticality with a twist - interplay of correlations and Kohn anomalies in three dimensions
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• Phonons and d-wave pairing in the two-dimensional Hubbard model
• Interacting electrons on trilayer honeycomb lattices
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Derivation of exact flow equations from the self-consistent parquet relations
• Stability of self-consistent solutions for the Hubbard model at intermediate and strong coupling
• Correlated starting points for the functional renormalization group
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Angle-Resolved Loss of Landau Quasiparticles in 2D Hubbard Model
• Retardation effects in the Holstein-Hubbard chain at half-filling
• Self-energy feedback and frequency-dependent interactions in the functional renormalization group flow for the two-dimensional Hubbard model
• Anomalous self-energy and Fermi surface quasi-splitting in the vicinity of a ferromagnetic instability
• Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution
• The two-loop functional renormalization-group approach to the one- and two-dimensional Hubbard model
• Precursors of the insulating state in the square lattice Hubbard model
• Self-energy effects in functional renormalization group flows of the two-dimensional $t$-$t^{\prime }$ Hubbard model away from van Hove filling
• Multiband Effects on Superconducting Instabilities Driven by Electron-Electron Interactions
• Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model
• Functional renormalization group study of an eight-band model for the iron arsenides
• Phase Diagram of the Holstein-Hubbard Two-Leg Ladder
• Effective three-particle interactions in low-energy models for multiband systems
• Fermi-edge singularity and the functional renormalization group

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• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
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• TU${}^2$FRG -- a scalable approach for truncated unity functional renormalization group in generic fermionic models
• Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• divERGe implements various Exact Renormalization Group examples
• Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Scaling theory for Mott-Hubbard transitions
• Taming pseudo-fermion functional renormalization for quantum spins: Finite-temperatures and the Popov-Fedotov trick
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Benchmark Calculations of Multiloop Pseudofermion fRG
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
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• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Fluctuation diagnostics of the finite temperature quasi-antiferromagnetic regime of the 2D Hubbard model
• KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model
• Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level
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• Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures
• Superconductivity from repulsion: Variational results for the 2D Hubbard model in the limit of weak interaction
• Review of recent developments of the functional renormalization group for systems out of equilibrium
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Quasi-particle functional Renormalisation Group calculations in the two-dimensional t-t'-Hubbard model
• 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
• Quantitative functional renormalization for three-dimensional quantum Heisenberg models
• Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism
• Kohn-Luttinger-like mechanism for unconventional charge density waves
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model
• Frequency Dependent Functional Renormalization Group for Interacting Fermionic Systems
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials