Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling

Abstract

We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.

References in corpus (71)

• The GW method
• Functional renormalization group approach to correlated fermion systems
• The nonperturbative functional renormalization group and its applications
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• The Hubbard model: A computational perspective
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• 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
• 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
• Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors I: General theory and quasiparticle properties
• Mott physics and spin fluctuations: a unified framework
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• 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
• A finite-frequency functional RG approach to the single impurity Anderson model
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Breakdown of traditional many-body theories for correlated electrons
• High-performance functional renormalization group calculations for interacting fermions
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Multiloop functional renormalization group for general models
• Multiloop functional renormalization group that sums up all parquet diagrams
• Flow Equations for the BCS-BEC Crossover
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Parquet approximation for the 4x4 Hubbard cluster
• Consistent partial bosonization of the extended Hubbard model
• Parquet decomposition calculations of the electronic self-energy
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Single-boson exchange decomposition of the vertex function
• Generic optical excitations of correlated systems: $\pi$-tons
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Competing order in correlated electron systems made simple: Consistent fusion of functional renormalization and mean-field theory
• 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
• Boson-Exchange Parquet Solver for dual fermions
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Renormalization group flow for fermionic superfluids at zero temperature
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Nonlocal correlations and spectral properties of the Falicov-Kimball model
• Parquet-like equations for the Hedin three-leg vertex
• Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Efficient Bethe-Salpeter equations' treatment in dynamical mean-field theory
• Renormalization of the BCS-BEC crossover by order parameter fluctuations
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• The two-loop functional renormalization-group approach to the one- and two-dimensional Hubbard model
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• Four-point vertex in the Hubbard model and partial bosonization
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• 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
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model
• Functional renormalization group for d-wave superconductivity in Hubbard type models
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Low energy singularities in the ground state of fermionic superfluids
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Parquet dual fermion approach for the Falicov-Kimball model
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling

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