Efficient parametrization of the vertex function,Ωscheme, and thet,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 obtained by a temperature RG flow in [12]. Instead of regularizing with temperature, we here use a soft frequency Ω-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.

Chirald-wave superconductivity in doped graphene

“…This can be done by using so-called N -patch discretizations [97,98,99], where the regions around the Brillouin zone points of interest are split up into angular sectors, and the coupling function is held constant within these patches. Another variant to capture more of the wave vector dependence is channel decompositions of the vertex [100,101], in particular, the so-called singular-mode fRG [44], which is described in a bit more detail below.…”

“…They used the so-called singular-mode fRG, which is based on the same flow equations as in the previously mentioned N -patch fRG, but uses a different representation for the electronic interactions. Rather than discretizing the wave vector dependence around the Fermi surface and working with a coupling function that depends on three wave vectors, singular-mode fRG uses a channel decomposition (see also [100]) and form factors to express the wave vector dependence of the coupling function. This way a better resolution of the modes away from the Fermi surface and of the longwavelength ordering tendencies is obtained.…”

Topological superconducting phase in the vicinity of ferromagnetic phases

“…All calculations are carried out using the singular-mode functional renormalization group (SM-FRG) method. 27,28 More details on this method can be found in the Appendix.…”

“…(A1) is exact if the form factors are complete, but in practice a few of them are often enough to capture the leading instabilities. 27,28 Because of full antisymmetry, the matrices C and D satisfy D = −C, and are therefore not independent. In the following D is used for bookkeeping purpose.…”

Critical behavior of the (2+1)-dimensional Thirring model

“…A solution of the Fierz ambiguity using the functional RG in a partially bosonized setting [66] requires dynamical bosonization [67] as will become important below. An alternative approach in the purely fermionic description employs a new parametrization of the momentum structure of the fourfermi couplings, see [68]. The particular choice of couplingsḡ andg as used in [49] is recovered for α 1 = −ḡ 2 − 3ḡ 4 and α 2 = −ḡ 4 and the definitionḡ…”