On the fulfillment of Ward identities in the functional renormalization group approach

Details On the fulfillment of Ward identities in the functional renormalization group approach On the fulfillment of Ward identities in the functional renormalization group approach

2004-02-24

arxiv.org/abs/cond-mat/0402602v2

Phys. Rev. B 70, 115109 (2004)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 1 figure, RevTex

Scientific paper

10.1103/PhysRevB.70.115109

I consider the fulfillment of conservation laws and Ward identities in the one- and two-loop functional renormalization group approach. It is shown that in a one-particle irreducible scheme of this approach Ward identities are fulfilled only with the accuracy of the neglected two-loop terms O(V^3) at one-loop order, and with the accuracy O(V^4) at two-loop order (V is the effective interaction vertex at scale \Lambda). The one-particle self-consistent version of the two-loop RG equations which leads to smaller errors in Ward identities due to the absence of the terms with non-overlapping loops, is proposed. In particular, these modified equations exactly satisfy Ward identities in the ladder approximation.

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