Quantitative functional renormalization-group description of the two-dimensional Hubbard model

Abstract

Using a leading algorithmic implementation of the functional renormalization group (fRG) for interacting fermions on two-dimensional lattices, we provide a detailed analysis of its quantitative reliability for the Hubbard model. In particular, we show that the recently introduced multiloop extension of the fRG flow equations for the self-energy and two-particle vertex allows for a precise match with the parquet approximation also for two-dimensional lattice problems. The refinement with respect to previous fRG-based computation schemes relies on an accurate treatment of the frequency and momentum dependences of the two-particle vertex, which combines a proper inclusion of the high-frequency asymptotics with the so-called truncated unity fRG for the momentum dependence. The adoption of the latter scheme requires, as an essential step, a consistent modification of the flow equation of the self-energy. We quantitatively compare our fRG results for the self-energy and momentum-dependent susceptibilities and the corresponding solution of the parquet approximation to determinant quantum Monte Carlo data, demonstrating that the fRG is remarkably accurate up to moderate interaction strengths. The presented methodological improvements illustrate how fRG flows can be brought to a quantitative level for two-dimensional problems, providing a solid basis for the application to more general systems.

19 pages, 21 figures

References in corpus (69)

• Exact evolution equation for the effective potential
• Renormalization Group Approach to Interacting Fermions
• Functional renormalization group approach to correlated fermion systems
• Topological Mott Insulators
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Funtional Renormalization Group Study of the Pairing Symmetry and Pairing Mechanism of the FeAs Based High Temperature Superconductors
• A Numerical Renormalization Group Study of the Superconducting and Spin Density Wave Instabilities in MFeAsO${}_{1-x}$F${}_x$ Compounds
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Competing many-body instabilities and unconventional superconductivity in graphene
• Density waves and Cooper pairing on the honeycomb lattice
• Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• 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
• From infinite to two dimensions through the functional renormalization group
• Nature of magnetic excitations in superconducting BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$
• Local magnetic moments in iron and nickel at ambient and Earth's core conditions
• Critical properties of the half-filled Hubbard model in three dimensions
• A finite-frequency functional RG approach to the single impurity Anderson model
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• 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
• Weakly correlated electrons on a square lattice: a renormalization group theory
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Multiloop functional renormalization group that sums up all parquet diagrams
• Multiloop functional renormalization group for general models
• Conductivity in the square lattice Hubbard model at high temperatures: importance of vertex corrections
• Quasiparticle anisotropy and pseudogap formation from the weak-coupling renormalization group point of view
• Quantum dynamical screening of the local magnetic moment in Fe-based superconductors
• Continuous renormalization for fermions and Fermi liquid theory
• Functional renormalization group for Luttinger liquids with impurities
• Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections
• Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Self-energy flows in the two-dimensional repulsive Hubbard model
• Finite-temperature Auxiliary-Field Quantum Monte Carlo: Self-Consistent Constraint and Systematic Approach to Low Temperatures
• Truncated Unity Parquet Solver
• Generic optical excitations of correlated systems: $\pi$-tons
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• Derivation of exact flow equations from the self-consistent parquet relations
• Self-energy and vertex functions from hybridization expansion continuous-time quantum Monte Carlo for impurity models with retarded interaction
• Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies
• Correlated spinless fermions on the honeycomb lattice revisited
• Correlated starting points for the functional renormalization group
• Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Dynamical vertex approximation for the two-dimensional Hubbard model
• The two-loop functional renormalization-group approach to the one- and two-dimensional Hubbard model
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Characteristic Timescales of the Local Moment Dynamics in Hund's-metals
• Screened moments and absence of ferromagnetism in FeAl
• Pseudogap opening in the two-dimensional Hubbard model: A functional renormalization group analysis
• Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems
• $\kappa -(BEDT-TTF{)}_{2}X$ organic crystals: superconducting versus antiferromagnetic instabilities in an anisotropic triangular lattice Hubbard model
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Reaching the continuum limit in finite-temperature ab initio field-theory computations in many-fermion systems
• Self-energy effects in functional renormalization group flows of the two-dimensional $t$-$t^{\prime }$ Hubbard model away from van Hove filling
• Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
• Dynamically enhanced magnetic incommensurability: Effects of local dynamics on non-local spin-correlations in a strongly correlated metal
• Hierarchical Parallelisation of Functional Renormalisation Group Calculations -- hp-fRG
• Schwinger-Dyson Renormalization Group

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• 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
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