Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group

Abstract

We present a consistent fusion of functional renormalization group and mean-field theory which explicitly introduces a bosonic field via a Hubbard-Stratonovich transformation at the critical scale, at which the order sets in. We show that a minimal truncation of the flow equations, that neglects order parameter fluctuations, is integrable and fulfills fundamental constraints as the Goldstone theorem and the Ward identity connected with the broken global symmetry. To introduce the bosonic field, we present a technique to factorize the most singular part of the vertex, even when the full dependence on all its arguments is retained. We test our method on the two-dimensional attractive Hubbard model at half-filling and calculate the superfluid gap as well as the Yukawa couplings and residual two fermion interactions in the ordered phase as functions of fermionic Matsubara frequencies. Furthermore, we analyze the gap and the condensate fraction for weak and moderate couplings and compare our results with previous functional renormalization group studies, and with quantum Monte Carlo data. Our formalism constitutes a convenient starting point for the inclusion of order parameter fluctuations by keeping a full, non simplified, dependence on fermionic momenta and/or frequencies.

arXiv comment20 pages, 10 figures

References in corpus (61)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Functional renormalization group approach to correlated fermion systems
• Renormalization group analysis of the 2D Hubbard model
• Deviations from Fermi-liquid behavior above $T_c$ in 2D short coherence length superconductors
• 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
• On the fulfillment of Ward identities in the functional renormalization group approach
• Dual boson approach to collective excitations in correlated fermionic systems
• From infinite to two dimensions through the functional renormalization group
• Dynamical mean-field theory for pairing and spin gap in the attractive Hubbard model
• Functional renormalization for spontaneous symmetry breaking in the Hubbard model
• Renormalization group flows into phases with broken symmetry
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Energetic balance of the superconducting transition across the BCS-Bose E instein crossover in the attractive Hubbard model
• High-performance functional renormalization group calculations for interacting fermions
• First-Order Pairing Transition and Single-Particle Spectral Function in the Attractive Hubbard Model
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Mott physics and spin fluctuations: a functional viewpoint
• Multiloop functional renormalization group that sums up all parquet diagrams
• Multiloop functional renormalization group for general models
• Flow Equations for the BCS-BEC Crossover
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Consistent partial bosonization of the extended Hubbard model
• Superconductivity in the two-dimensional $t$-$t^{\prime }$-Hubbard model
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Particle-hole fluctuations in the BCS-BEC Crossover
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Single-boson exchange decomposition of the vertex function
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Quantitative functional renormalization-group description of the two-dimensional Hubbard model
• Multiloop functional renormalization group for the two-dimensional Hubbard model: Loop convergence of the response functions
• 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
• Renormalization group flow for fermionic superfluids at zero temperature
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Effective Heisenberg model and exchange interaction for strongly correlated systems
• Parquet-like equations for the Hedin three-leg vertex
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model
• Functional renormalization group approach to the Anderson impurity model
• Dynamical vertex approximation for the attractive Hubbard model
• Renormalization of the BCS-BEC crossover by order parameter fluctuations
• Fermion-boson vertex within Dynamical Mean-Field Theory
• Effective interactions and fluctuation effects in spin-singlet superfluids
• Dual Boson approach with instantaneous interaction
• Four-point vertex in the Hubbard model and partial bosonization
• Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model
• Spectral function of the Anderson impurity model at finite temperatures
• Generation of d-wave coupling in the two-dimensional Hubbard model from functional renormalization
• Solution of the Anderson impurity model via the functional renormalization group
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Breakdown of the Fermi-liquid regime in the 2D Hubbard model from a two-loop field-theoretical renormalization group approach
• Low energy singularities in the ground state of fermionic superfluids
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
• Study of the superconducting order parameter in the negative-$U$ 2D-Hubbard model by grand-canonical twist-averaged boundary conditions
• Summing parquet diagrams using the functional renormalization group: X-ray problem revisited
• Functional renormalization group study of fluctuation effects in fermionic superfluids
• Critical pairing fluctuations in the normal state of a superconductor: pseudogap and quasi-particle damping

Cited by in corpus (9)

• Boson-Exchange Parquet Solver for dual fermions
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Interaction-driven first-order and higher-order topological superconductivity
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order