Fulfillment of Ward identities in the functional renormalization group approach

A. A. Katanin

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105 Citations (Scopus)


We 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 Λ3) at one-loop order, and with the accuracy O(VΛ4) at two-loop order (VΛ is the effective interaction vertex at scale Λ). The one-particle self-consistent version of the two-loop renormalization group equations which leads to smaller errors in Ward identities due to the absence of the terms with nonoverlapping loops, is proposed. In particular, these modified equations exactly satisfy Ward identities in the ladder approximation.

Original languageEnglish
Article number115109
Pages (from-to)115109-1-115109-5
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
Publication statusPublished - Sep 2004
Externally publishedYes


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