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

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

2008-12-19

arxiv.org/abs/0812.3824v2

Physics

Condensed Matter

Strongly Correlated Electrons

33 pages, 11 figures, references added

Scientific paper

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.

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