Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling

Abstract

We propose a new parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak coupling instabilities of the two-dimensional Hubbard model at Van Hove filling, as they were previously obtained by a temperature RG flow. Instead of regularizing with temperature, we here use a soft frequency $\Omega$-regularization that likewise does not artificially suppress ferromagnetism. Besides being more efficient than previous N-patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.

33 pages, 11 figures, references added

References in corpus (18)

• On the fulfillment of Ward identities in the functional renormalization group approach
• Renormalization group flows into phases with broken symmetry
• A finite-frequency functional RG approach to the single impurity Anderson model
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
• Renormalization group analysis of magnetic and superconducting instabilities near van Hove band fillings
• Interaction flow method for many-fermion systems
• Quasiparticle anisotropy and pseudogap formation from the weak-coupling renormalization group point of view
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling
• Flow of the quasiparticle weight in the N-patch renormalization group scheme
• Renormalization group flow for fermionic superfluids at zero temperature
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Determinant Bounds and the Matsubara UV Problem of Many-Fermion Systems
• Weak ferromagnetism and other instabilities of the two-dimensional t-t' Hubbard model at Van Hove fillings
• Generation of d-wave coupling in the two-dimensional Hubbard model from functional renormalization
• Dynamical Adjustment of Propagators in Renormalization Group Flows
• Eliashberg equations derived from the functional renormalization group

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