Normal fermions: Partial bosonization in the forward scattering channel

Abstract

The advantage of the one-loop patching approximation discussed in Sect. 10.5 is that this approach is completely unbiased, because it retains on equal footing the RG flow of all marginal couplings related to the four-point vertex. An obvious disadvantage of the one-loop patching approximation is the fact that it breaks down when at least one of the marginal couplings becomes large, which usually happens when the RG cutoff Λ reaches a finite scale Λ c . For the two-dimensional Hubbard model with nearest-neighbor hopping we have explicitly calculated the scale Λ c in Sect. 10.5.4, see Fig. 10.14. Although it seems reasonable to assume that the coupling which diverges at the smallest RG scale indicates the dominant instability of the system, there is no proof that this is always the case. © 2010 Springer-Verlag Berlin Heidelberg.